Metrics for 2sqrt (example 3.1)

analyze3.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
0%	0%	25%	75%	0%	0%	0%	1
50%	12.5%	12.5%	75%	0%	0%	0%	2
75%	18.7%	6.2%	75%	0%	0%	0%	3
87.5%	21.9%	3.1%	75%	0%	0%	0%	4
93.8%	23.4%	1.6%	75%	0%	0%	0%	5
96.9%	24.2%	0.8%	75%	0%	0%	0%	6
98.4%	24.6%	0.4%	75%	0%	0%	0%	7
99.2%	24.8%	0.2%	75%	0%	0%	0%	8
99.6%	24.9%	0.1%	75%	0%	0%	0%	9
99.8%	24.9%	0%	75%	0%	0%	0%	10
99.9%	25%	0%	75%	0%	0%	0%	11
100%	25%	0%	75%	0%	0%	0%	12

Compiler

Compiled 15 to 10 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

...c/correct-round.rkt:119:19: 0.0ms (0% of total)

const: 0.0ms (0% of total)

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

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

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

sample2.6s (23.5%)

Results

1.2s	3240×	2	valid
1.0s	4842×	1	valid
17.0ms	174×	0	valid

Precisions

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

ival-add: 454.0ms (27.9% of total)

ival-sqrt: 338.0ms (20.8% of total)

...c/correct-round.rkt:119:19: 216.0ms (13.3% of total)

backward-pass: 200.0ms (12.3% of total)

ival->: 184.0ms (11.3% of total)

ival-sub: 148.0ms (9.1% of total)

ival-and: 40.0ms (2.5% of total)

ival-<: 28.0ms (1.7% of total)

const: 19.0ms (1.2% of total)

Bogosity

preprocess52.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

270×	`sum3-define`
244×	`fnmadd-define`
184×	`fmsub-define`
168×	`fnmsub-define`
168×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	25	24
2	52	23
3	99	23
4	190	23
5	387	23
6	579	23
7	755	23
8	849	23
9	955	23
10	1033	23
11	1039	23
0	6	7
1	11	7
2	15	7
3	22	7
4	32	7
5	64	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (sqrt (+ x 1)) (sqrt x))

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

Call 2

Inputs
(- (sqrt (+ x 1)) (sqrt x))
(- (sqrt (+ (neg x) 1)) (sqrt (neg x)))
(neg (- (sqrt (+ (neg x) 1)) (sqrt (neg x))))

Outputs
(- (sqrt (+ x 1)) (sqrt x))
(- (sqrt (+ (neg x) 1)) (sqrt (neg x)))
(- (sqrt (- 1 x)) (sqrt (neg x)))
(neg (- (sqrt (+ (neg x) 1)) (sqrt (neg x))))
(- (sqrt (neg x)) (sqrt (- 1 x)))

explain233.0ms (2.1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
253	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`x`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 x)`
0	-	-	`(+.f64 x #s(literal 1 binary64))`

Results

135.0ms	202×	2	valid
64.0ms	296×	1	valid
1.0ms	14×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-sqrt: 25.0ms (37.7% of total)

backward-pass: 18.0ms (27.1% of total)

ival-sub: 13.0ms (19.6% of total)

ival-add: 9.0ms (13.6% of total)

const: 1.0ms (1.5% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
x
1
(sqrt x)

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

localize76.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

35.0ms	101×	2	valid
30.0ms	148×	1	valid
1.0ms	7×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sqrt: 10.0ms (40.3% of total)

backward-pass: 7.0ms (28.2% of total)

ival-add: 4.0ms (16.1% of total)

ival-sub: 3.0ms (12.1% of total)

const: 1.0ms (4% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

Outputs
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>

Calls

12 calls:

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

rewrite335.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

2088×	`-lowering-.f32`
2088×	`-lowering-.f64`
1794×	`fma-lowering-fma.f32`
1794×	`fma-lowering-fma.f64`
1676×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	39	16
2	303	16
3	3722	16
0	8049	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

Inputs
(- (sqrt (+ x 1)) (sqrt x))
(sqrt (+ x 1))
(+ x 1)
(sqrt x)

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

simplify224.0ms (2%)

Algorithm

1×	egg-herbie

Rules

2970×	`-lowering-.f32`
2970×	`-lowering-.f64`
2056×	`+-lowering-+.f64`
2056×	`+-lowering-+.f32`
1514×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1039	376
3	3226	373
4	7122	373
0	8132	373

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

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

eval72.0ms (0.6%)

Compiler: Compiled 5806 to 837 computations (85.6% saved)

prune45.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	260	8	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	260	9	269

Accuracy

99.9%

Counts

269 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.7%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 3/2 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
▶	6.2%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
▶	98.3%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	9.4%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	7.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	7.3%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
	97.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 318 to 182 computations (42.8% saved)

simplify255.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 3/2 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
✓	cost-diff	0	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Rules

3670×	`-lowering-.f32`
3670×	`-lowering-.f64`
2630×	`--lowering--.f32`
2630×	`--lowering--.f64`
1978×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	323
1	103	297
2	279	297
3	1652	297
4	3423	297
5	4686	297
0	8150	297

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))
(* -1/8 (sqrt (/ 1 x)))
-1/8
(sqrt (/ 1 x))
(/ 1 x)
1
x
(* (sqrt x) 1/2)
(sqrt x)
1/2
(- 1 (sqrt x))
1
(sqrt x)
x
(/ 1 (/ 1 (- (pow (+ x 1) 1/2) (sqrt x))))
1
(/ 1 (- (pow (+ x 1) 1/2) (sqrt x)))
(- (pow (+ x 1) 1/2) (sqrt x))
(pow (+ x 1) 1/2)
(+ x 1)
x
1/2
(sqrt x)
(/ (- (pow (+ x 1) 3/2) (pow x 3/2)) (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))))
(- (pow (+ x 1) 3/2) (pow x 3/2))
(pow (+ x 1) 3/2)
(+ x 1)
x
1
3/2
(pow x 3/2)
(+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))
(sqrt (* x (+ x 1)))
(* x (+ x 1))
(+ x (+ x 1))
(/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))
(- (pow (+ x 1) 9/2) (pow x 9/2))
(pow (+ x 1) 9/2)
(+ x 1)
x
1
9/2
(pow x 9/2)
(* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1)))))
(+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))
(sqrt (* x (+ x 1)))
(* x (+ x 1))
(+ x (+ x 1))
(+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))
(+ (* x (* x x)) (pow (* x (+ x 1)) 3/2))
(* x (* x x))
(* x x)
(pow (* x (+ x 1)) 3/2)
3/2
(* (+ x 1) (* (+ x 1) (+ x 1)))
(* (+ x 1) (+ x 1))

Outputs
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
-1/8
#s(literal -1/8 binary64)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(* (sqrt x) 1/2)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
1/2
#s(literal 1/2 binary64)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)
x
(/ 1 (/ 1 (- (pow (+ x 1) 1/2) (sqrt x))))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
1
#s(literal 1 binary64)
(/ 1 (- (pow (+ x 1) 1/2) (sqrt x)))
(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(- (pow (+ x 1) 1/2) (sqrt x))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(pow (+ x 1) 1/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)
x
1/2
#s(literal 1/2 binary64)
(sqrt x)
(sqrt.f64 x)
(/ (- (pow (+ x 1) 3/2) (pow x 3/2)) (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 x #s(literal 2 binary64)))))
(- (pow (+ x 1) 3/2) (pow x 3/2))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(pow (+ x 1) 3/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)
x
1
#s(literal 1 binary64)
3/2
#s(literal 3/2 binary64)
(pow x 3/2)
(pow.f64 x #s(literal 3/2 binary64))
(+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 x #s(literal 2 binary64))))
(sqrt (* x (+ x 1)))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(* x (+ x 1))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(+ x (+ x 1))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))
(/.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 x #s(literal 2 binary64)))) (+.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)) (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))))
(- (pow (+ x 1) 9/2) (pow x 9/2))
(-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))
(pow (+ x 1) 9/2)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)
x
1
#s(literal 1 binary64)
9/2
#s(literal 9/2 binary64)
(pow x 9/2)
(pow.f64 x #s(literal 9/2 binary64))
(* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1)))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 x #s(literal 2 binary64)))) (+.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)) (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))))
(+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))
(+.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 x #s(literal 2 binary64))))
(sqrt (* x (+ x 1)))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(* x (+ x 1))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(+ x (+ x 1))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))
(+.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)) (+.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(+ (* x (* x x)) (pow (* x (+ x 1)) 3/2))
(+.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)))
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.f64 x x)
(pow (* x (+ x 1)) 3/2)
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64))
3/2
#s(literal 3/2 binary64)
(* (+ x 1) (* (+ x 1) (+ x 1)))
(.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(* (+ x 1) (+ x 1))
(*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))

localize700.0ms (6.3%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	53.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	32.1%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 3/2 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))
✓	accuracy	18.7%	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))
✓	accuracy	99.8%	(+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.4%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	53.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	7.0%	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	7.5%	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.5%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Results

298.0ms	151×	1	valid
274.0ms	91×	2	valid
25.0ms	6×	3	valid
6.0ms	8×	0	valid

Compiler

Compiled 382 to 40 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 347.0ms

ival-pow: 173.0ms (49.9% of total)

backward-pass: 56.0ms (16.1% of total)

ival-mult: 38.0ms (11% of total)

ival-div: 27.0ms (7.8% of total)

ival-add: 18.0ms (5.2% of total)

ival-sub: 16.0ms (4.6% of total)

ival-sqrt: 16.0ms (4.6% of total)

const: 2.0ms (0.6% of total)

series38.0ms (0.3%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)>
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (- 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ 1 (/ 1 (- (pow (+ x 1) 1/2) (sqrt x))))>
#<alt (/ 1 (- (pow (+ x 1) 1/2) (sqrt x)))>
#<alt (- (pow (+ x 1) 1/2) (sqrt x))>
#<alt (pow (+ x 1) 1/2)>
#<alt (/ (- (pow (+ x 1) 3/2) (pow x 3/2)) (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))))>
#<alt (- (pow (+ x 1) 3/2) (pow x 3/2))>
#<alt (pow (+ x 1) 3/2)>
#<alt (+ x 1)>
#<alt (/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))>
#<alt (- (pow (+ x 1) 9/2) (pow x 9/2))>
#<alt (pow (+ x 1) 9/2)>
#<alt (sqrt (* x (+ x 1)))>
#<alt (+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))>

Outputs
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (- 1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* x (- (/ 1 x) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt (/ 1 (- 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (+ (* -5/32 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))))) (pow x 6))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))))))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 3/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x))))) (* 2 (/ (- (* 3/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (* 3/8 (/ 1 (+ 1 (sqrt x))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (- (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (* 1/4 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* 1/6 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (+ (* -1/48 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2)))))) x)>
#<alt (/ (- (+ (* -3/4 (sqrt (/ 1 (pow x 3)))) (+ (* 1/6 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (+ (* -1/24 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/48 (sqrt (/ 1 (pow x 3)))) (+ (* 1/96 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/2 (/ (- (* 1/6 (* (sqrt x) (- 1 (* 9/4 x)))) (+ (* -1/48 (sqrt x)) (* 1/2 (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2))))))))) x)>
#<alt (* -3/2 (* (sqrt (/ 1 x)) (/ 1 (- (pow (sqrt -1) 2) 2))))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) x))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (* 9/4 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 2))))) (+ (* -1/8 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 2)))) (+ (* 3/32 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) (- (pow (sqrt -1) 2) 2)))))) x)) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2))))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) x))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))>
#<alt 1>
#<alt (+ 1 (* x (- 3/2 (sqrt x))))>
#<alt (+ 1 (* x (- (+ 3/2 (* 3/8 x)) (sqrt x))))>
#<alt (+ 1 (* x (- (+ 3/2 (* x (+ 3/8 (* -1/16 x)))) (sqrt x))))>
#<alt (* 3/2 (sqrt x))>
#<alt (+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x))))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x)))))>
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#<alt (* 3/2 (sqrt x))>
#<alt (+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) x)) (* 3/2 (sqrt x)))>
#<alt (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1 (/ (+ (* -9/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) x))) x)) (* 3/2 (sqrt x)))>
#<alt 1>
#<alt (+ 1 (* 3/2 x))>
#<alt (+ 1 (* x (+ 3/2 (* 3/8 x))))>
#<alt (+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))>
#<alt (sqrt (pow x 3))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (* 3/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5)))))))>
#<alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 39/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (+ (* 39/8 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 73/16 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2)))) (+ (* 3/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* 6 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 39/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))) (+ 1 (sqrt x))) (/ (* (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 2 (+ 3 (sqrt x))) (* 3 (+ 1 (sqrt x))))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (- (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x)))) (sqrt (/ 1 x))) x)>
#<alt (/ (- (+ (* 1/18 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x))))) (+ (sqrt (/ 1 x)) (+ (* 11/12 (sqrt (/ 1 (pow x 3)))) (* 2 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 2)))))) x)>
#<alt (/ (- (+ (* 1/18 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/18 (* (sqrt (/ 1 (pow x 5))) (- 126 (* 162 x)))) (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x)))))) (+ (sqrt (/ 1 x)) (+ (* 5/12 (sqrt (/ 1 (pow x 5)))) (+ (* 11/12 (sqrt (/ 1 (pow x 3)))) (+ (* 11/6 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 3))) (+ (* 2 (/ (- (* 1/18 (* (sqrt x) (- 84 (* 81/4 x)))) (+ (* 11/12 (sqrt x)) (* 2 (- (* 2 (sqrt x)) (sqrt x))))) (pow x 3))) (* 2 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 2))))))))) x)>
#<alt (* 9/2 (* (sqrt (/ 1 x)) (/ 1 (- (pow (sqrt -1) 2) 2))))>
#<alt (* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))>
#<alt (* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) x)) (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))>
#<alt (* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt x) (/ (- (* -162 (/ x (pow (sqrt -1) 2))) 126) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (+ (* -1 (/ (* (- (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2)) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (- (* 17/16 (- (pow (sqrt -1) 2) 2)) (+ 63/16 (+ (* 1/16 (/ 1 (pow (sqrt -1) 4))) (* 3/16 (/ 1 (pow (sqrt -1) 2)))))) (pow (- (pow (sqrt -1) 2) 2) 2))))))) x)) (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2))))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) x)) (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))>
#<alt 1>
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#<alt (* (pow x 3) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x)))))>
#<alt (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x))))))>
#<alt (* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- 126 (* 162 x)))) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x)))))))>
#<alt (* -9/2 (sqrt (pow x 7)))>
#<alt (* -1 (* (pow x 3) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x))))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x)) (* 9/2 (sqrt x)))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (- (* -162 (/ x (pow (sqrt -1) 2))) 126))) (* 1/2 (* (sqrt x) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x))) x)) (* 9/2 (sqrt x)))))>
#<alt 1>
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#<alt (+ 1 (* x (+ 9/2 (* x (+ 63/8 (* 105/16 x))))))>
#<alt (sqrt (pow x 9))>
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#<alt (* -1 (* (sqrt (pow x 9)) (pow (sqrt -1) 2)))>
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#<alt (* -1 (* (pow x 5) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (+ (* 18 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 2 (* 1/2 (sqrt x))))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 2 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))))>
#<alt (* 3 x)>
#<alt (* x (+ 3 (* 3/2 (/ 1 x))))>
#<alt (* x (- (+ 3 (* 3/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 3 (+ (* 3/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (+ 2 (* 3/2 (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ 3/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))>

Calls

57 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))
4.0ms	x	@	-inf	(pow (+ x 1) 9/2)
3.0ms	x	@	0	(* -1/8 (sqrt (/ 1 x)))
3.0ms	x	@	-inf	(/ (- (pow (+ x 1) 3/2) (pow x 3/2)) (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))))
3.0ms	x	@	0	(/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))

rewrite343.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2944×	`-lowering-.f32`
2944×	`-lowering-.f64`
2360×	`fma-lowering-fma.f32`
2360×	`fma-lowering-fma.f64`
1864×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	123
1	293	115
2	2770	113
0	9047	113

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 862

Calls

Call 1

Inputs
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
(+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))
(* -1/8 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(- 1 (sqrt x))
(sqrt x)
(/ 1 (/ 1 (- (pow (+ x 1) 1/2) (sqrt x))))
(/ 1 (- (pow (+ x 1) 1/2) (sqrt x)))
(- (pow (+ x 1) 1/2) (sqrt x))
(pow (+ x 1) 1/2)
(/ (- (pow (+ x 1) 3/2) (pow x 3/2)) (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))))
(- (pow (+ x 1) 3/2) (pow x 3/2))
(pow (+ x 1) 3/2)
(+ x 1)
(/ (- (pow (+ x 1) 9/2) (pow x 9/2)) (* (+ (sqrt (* x (+ x 1))) (+ x (+ x 1))) (+ (+ (* x (* x x)) (pow (* x (+ x 1)) 3/2)) (* (+ x 1) (* (+ x 1) (+ x 1))))))
(- (pow (+ x 1) 9/2) (pow x 9/2))
(pow (+ x 1) 9/2)
(sqrt (* x (+ x 1)))
(+ (sqrt (* x (+ x 1))) (+ x (+ x 1)))

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

simplify380.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

5164×	`+-lowering-+.f64`
5164×	`+-lowering-+.f32`
4126×	`-lowering-.f32`
4126×	`-lowering-.f64`
2042×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	805	4864
1	2711	3765
0	8411	3765

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/ 1 (- 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (+ (* -5/32 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))))) (pow x 6))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))))))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ 1 (+ 1 (sqrt x)))
(+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 3/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (+ (* -1 (* x (+ (* 1/16 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x))))) (* 2 (/ (- (* 3/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (* 3/8 (/ 1 (+ 1 (sqrt x))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 2 (/ (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x)))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (- (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))) (* 1/4 (sqrt (/ 1 x)))) x)
(/ (- (+ (* 1/6 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (+ (* -1/48 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2)))))) x)
(/ (- (+ (* -3/4 (sqrt (/ 1 (pow x 3)))) (+ (* 1/6 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (+ (* -1/24 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/48 (sqrt (/ 1 (pow x 3)))) (+ (* 1/96 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 x))) (+ (* 1/2 (/ (- (* 1/6 (* (sqrt x) (- 1 (* 9/4 x)))) (+ (* -1/48 (sqrt x)) (* 1/2 (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x)))))) (pow x 3))) (* 1/2 (/ (- (* 1/2 (sqrt x)) (* 1/4 (sqrt x))) (pow x 2))))))))) x)
(* -3/2 (* (sqrt (/ 1 x)) (/ 1 (- (pow (sqrt -1) 2) 2))))
(* -1 (/ (+ (* -1 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))
(* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) x))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))
(* -1 (/ (+ (* -1 (/ (- (+ (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (* 9/4 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 2))))) (+ (* -1/8 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 2)))) (+ (* 3/32 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) (- (pow (sqrt -1) 2) 2)))))) x)) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2))))) (+ (* -3/16 (* (sqrt x) (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 2) 2))))) (* 3/2 (/ (- (* -3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) (- (pow (sqrt -1) 2) 2))))) x))) (* 9/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 2) 2))))) x)) (* 3/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) x))
1
(+ 1 (* x (- 3/2 (sqrt x))))
(+ 1 (* x (- (+ 3/2 (* 3/8 x)) (sqrt x))))
(+ 1 (* x (- (+ 3/2 (* x (+ 3/8 (* -1/16 x)))) (sqrt x))))
(* 3/2 (sqrt x))
(+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x))))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x)))))
(+ (* -9/4 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x))))))
(* 3/2 (sqrt x))
(+ (* 3/2 (sqrt x)) (* 3/2 (sqrt (/ 1 x))))
(+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) x)) (* 3/2 (sqrt x)))
(+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1 (/ (+ (* -9/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt x) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) x))) x)) (* 3/2 (sqrt x)))
1
(+ 1 (* 3/2 x))
(+ 1 (* x (+ 3/2 (* 3/8 x))))
(+ 1 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(sqrt (pow x 3))
(* (pow x 2) (+ (sqrt (/ 1 x)) (* 3/2 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5)))))))
(* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 (pow x 5))))))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(/ 1 (+ 1 (sqrt x)))
(+ (* x (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 39/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 3/2 (/ 1 (+ 1 (sqrt x)))) (* x (- (+ (* 39/8 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 73/16 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2)))) (+ (* 3/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* 6 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 39/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))) (+ 1 (sqrt x))) (/ (* (+ (* 1/2 (sqrt (/ 1 x))) (+ (* 2 (+ 3 (sqrt x))) (* 3 (+ 1 (sqrt x))))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))))) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (+ (* 2 (/ (+ 3 (sqrt x)) (pow (+ 1 (sqrt x)) 2))) (/ (* (+ 2 (* (+ 1 (sqrt x)) (+ 3 (sqrt x)))) (- (* 3/2 (/ 1 (+ 1 (sqrt x)))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (+ 1 (sqrt x)))))))) (+ (* 2 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (- (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x)))) (sqrt (/ 1 x))) x)
(/ (- (+ (* 1/18 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x))))) (+ (sqrt (/ 1 x)) (+ (* 11/12 (sqrt (/ 1 (pow x 3)))) (* 2 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 2)))))) x)
(/ (- (+ (* 1/18 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/18 (* (sqrt (/ 1 (pow x 5))) (- 126 (* 162 x)))) (+ (* 1/2 (sqrt x)) (* 2 (sqrt (/ 1 x)))))) (+ (sqrt (/ 1 x)) (+ (* 5/12 (sqrt (/ 1 (pow x 5)))) (+ (* 11/12 (sqrt (/ 1 (pow x 3)))) (+ (* 11/6 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 3))) (+ (* 2 (/ (- (* 1/18 (* (sqrt x) (- 84 (* 81/4 x)))) (+ (* 11/12 (sqrt x)) (* 2 (- (* 2 (sqrt x)) (sqrt x))))) (pow x 3))) (* 2 (/ (- (* 2 (sqrt x)) (sqrt x)) (pow x 2))))))))) x)
(* 9/2 (* (sqrt (/ 1 x)) (/ 1 (- (pow (sqrt -1) 2) 2))))
(* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))
(* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) x)) (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))
(* -1 (/ (+ (* -9/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt x) (/ (- (* -162 (/ x (pow (sqrt -1) 2))) 126) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (+ (* -1 (/ (* (- (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2)))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2)) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (- (* 17/16 (- (pow (sqrt -1) 2) 2)) (+ 63/16 (+ (* 1/16 (/ 1 (pow (sqrt -1) 4))) (* 3/16 (/ 1 (pow (sqrt -1) 2)))))) (pow (- (pow (sqrt -1) 2) 2) 2))))))) x)) (* -1/2 (* (sqrt x) (/ (- 84 (* -81/4 (/ x (pow (sqrt -1) 2)))) (- (pow (sqrt -1) 2) 2))))) (+ (* -1 (/ (* (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (- (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2)))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2)))))) (- (pow (sqrt -1) 2) 2))) (* 9/2 (* (sqrt x) (/ (+ 9/4 (+ (* -21/8 (- (pow (sqrt -1) 2) 2)) (* 1/8 (/ 1 (pow (sqrt -1) 2))))) (pow (- (pow (sqrt -1) 2) 2) 2)))))) x)) (* 18 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 2))))) (* 9/2 (* (sqrt x) (/ (- (* 3/2 (- (pow (sqrt -1) 2) 2)) 3/2) (pow (- (pow (sqrt -1) 2) 2) 2))))) x))) x))
1
(+ 1 (* 9/2 x))
(+ 1 (* x (+ 9/2 (* 63/8 x))))
(+ 1 (* x (+ 9/2 (* x (+ 63/8 (* 105/16 x))))))
(* 9/2 (sqrt (pow x 7)))
(* (pow x 3) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x)))))
(* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x))))))
(* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- 126 (* 162 x)))) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x)))))))
(* -9/2 (sqrt (pow x 7)))
(* -1 (* (pow x 3) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x)) (* 9/2 (sqrt x)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (- (* -162 (/ x (pow (sqrt -1) 2))) 126))) (* 1/2 (* (sqrt x) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x))) x)) (* 9/2 (sqrt x)))))
1
(+ 1 (* 9/2 x))
(+ 1 (* x (+ 9/2 (* 63/8 x))))
(+ 1 (* x (+ 9/2 (* x (+ 63/8 (* 105/16 x))))))
(sqrt (pow x 9))
(* (pow x 5) (+ (sqrt (/ 1 x)) (* 9/2 (sqrt (/ 1 (pow x 3))))))
(* (pow x 5) (+ (sqrt (/ 1 x)) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* 18 (sqrt (/ 1 (pow x 5)))))))
(* (pow x 5) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 84 (* 81/4 x)))) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* 18 (sqrt (/ 1 (pow x 5))))))))
(* -1 (* (sqrt (pow x 9)) (pow (sqrt -1) 2)))
(* -1 (* (pow x 5) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* (pow x 5) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (+ (* 18 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 2 x)))
(+ 1 (+ (sqrt x) (* x (+ 2 (* 1/2 (sqrt x))))))
(+ 1 (+ (sqrt x) (* x (+ 2 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))))
(* 3 x)
(* x (+ 3 (* 3/2 (/ 1 x))))
(* x (- (+ 3 (* 3/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 3 (+ (* 3/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (- (pow (sqrt -1) 2) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (+ 2 (* 3/2 (/ 1 x))))))
(* -1 (* x (- (+ (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))
(* -1 (* x (- (+ (* -1 (/ (+ 3/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))

Outputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(.f64 #s(literal -1 binary64) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(.f64 #s(literal -1 binary64) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(.f64 #s(literal -1 binary64) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (neg.f64 x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (sqrt x))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
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(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 9/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 18 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 84 binary64) (.f64 x #s(literal -81/4 binary64)))))))
(* (pow x 3) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (- 84 (* 81/4 x)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (- 126 (* 162 x)))) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x)))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 84 binary64) (.f64 x #s(literal -81/4 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 #s(literal 126 binary64) (.f64 x #s(literal -162 binary64)))))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 9/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 18 binary64)))))
(* -9/2 (sqrt (pow x 7)))
(*.f64 #s(literal -9/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 7 binary64))))
(* -1 (* (pow x 3) (+ (* 9/2 (sqrt x)) (* 18 (sqrt (/ 1 x))))))
(.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 9/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 18 binary64))) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x)) (* 9/2 (sqrt x)))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (sqrt.f64 x) #s(literal 9/2 binary64)) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -18 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 84 binary64) (/.f64 (.f64 x #s(literal -81/4 binary64)) #s(literal 1 binary64)))))) x))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (- (* -162 (/ x (pow (sqrt -1) 2))) 126))) (* 1/2 (* (sqrt x) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) x))) x)) (* 9/2 (sqrt x)))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (sqrt.f64 x) #s(literal 9/2 binary64)) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -18 binary64)) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 (.f64 x #s(literal -162 binary64)) #s(literal -1 binary64)) #s(literal -126 binary64)))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 #s(literal 84 binary64) (/.f64 (*.f64 x #s(literal -81/4 binary64)) #s(literal 1 binary64))))) x)) x))))
1
#s(literal 1 binary64)
(+ 1 (* 9/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 9/2 binary64)))
(+ 1 (* x (+ 9/2 (* 63/8 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 9/2 binary64) (.f64 x #s(literal 63/8 binary64)))))
(+ 1 (* x (+ 9/2 (* x (+ 63/8 (* 105/16 x))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 9/2 binary64) (.f64 x (+.f64 #s(literal 63/8 binary64) (*.f64 x #s(literal 105/16 binary64)))))))
(sqrt (pow x 9))
(sqrt.f64 (pow.f64 x #s(literal 9 binary64)))
(* (pow x 5) (+ (sqrt (/ 1 x)) (* 9/2 (sqrt (/ 1 (pow x 3))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64))))
(* (pow x 5) (+ (sqrt (/ 1 x)) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* 18 (sqrt (/ 1 (pow x 5)))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 18 binary64)))))
(* (pow x 5) (+ (sqrt (/ 1 x)) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 84 (* 81/4 x)))) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* 18 (sqrt (/ 1 (pow x 5))))))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 18 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 84 binary64) (.f64 x #s(literal -81/4 binary64))))))))
(* -1 (* (sqrt (pow x 9)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal 9 binary64))))
(* -1 (* (pow x 5) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (* (pow x 5) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (+ (* 18 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 18 binary64)))) (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (* (pow x 5) (+ (* -1 (/ (+ (* -18 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 84 (* -81/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 9/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 9/2 binary64))) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -18 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 84 binary64) (/.f64 (.f64 x #s(literal -81/4 binary64)) #s(literal 1 binary64)))))) (.f64 x (.f64 x x)))) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64)))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (neg.f64 x))) x))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(-.f64 #s(literal 0 binary64) (.f64 x (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (neg.f64 x))) (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) x))))
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (+ (sqrt x) (* 2 x)))
(+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64))))
(+ 1 (+ (sqrt x) (* x (+ 2 (* 1/2 (sqrt x))))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(+ 1 (+ (sqrt x) (* x (+ 2 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))))
(+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))
(* 3 x)
(*.f64 x #s(literal 3 binary64))
(* x (+ 3 (* 3/2 (/ 1 x))))
(*.f64 x (+.f64 #s(literal 3 binary64) (/.f64 #s(literal 3/2 binary64) x)))
(* x (- (+ 3 (* 3/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 3 binary64) (+.f64 (/.f64 #s(literal 3/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* x (- (+ 3 (+ (* 3/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 #s(literal 3 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (+.f64 (/.f64 #s(literal 3/2 binary64) x) (/.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(* -1 (* x (- (pow (sqrt -1) 2) 2)))
(*.f64 x #s(literal 3 binary64))
(* -1 (* x (- (pow (sqrt -1) 2) (+ 2 (* 3/2 (/ 1 x))))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -3 binary64) (/.f64 #s(literal 3/2 binary64) x))))
(* -1 (* x (- (+ (* -1 (/ (+ 3/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))
(*.f64 (+.f64 (/.f64 (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/8 binary64) (neg.f64 x))) (neg.f64 x)) #s(literal -3 binary64)) (neg.f64 x))
(* -1 (* x (- (+ (* -1 (/ (+ 3/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 2)))
(.f64 (+.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 #s(literal 3/2 binary64) (/.f64 #s(literal 1/8 binary64) (neg.f64 x)))) (neg.f64 x)) #s(literal -3 binary64)) (neg.f64 x))

eval251.0ms (2.3%)

Compiler: Compiled 73428 to 4631 computations (93.7% saved)

prune205.0ms (1.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	1769	10	1779
Fresh	2	1	3
Picked	3	2	5
Done	0	1	1
Total	1774	14	1788

Accuracy

100.0%

Counts

1788 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.7%	(/.f64 (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x) x)
✓	6.2%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	5.5%	(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	9.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
▶	98.3%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
▶	97.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	98.2%	(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
▶	7.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	97.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
	97.2%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	98.1%	(.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
▶	97.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 324 to 216 computations (33.3% saved)

simplify146.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

1688×	`fnmadd-define`
1324×	`fma-define`
1202×	`fmsub-define`
1198×	`fnmsub-define`
924×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	138
1	37	133
2	66	133
3	121	133
4	197	133
5	295	133
6	441	133
7	605	133
8	815	133
9	1014	133
10	1365	133
11	2318	133
12	4893	133
13	5164	133
14	5727	133
15	5996	133
16	6135	133
17	6159	133
0	6159	133

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
(+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))
(/ -1/8 (sqrt x))
-1/8
(sqrt x)
x
(* (sqrt x) 1/2)
1/2
(* 1/2 (sqrt (/ 1 x)))
1/2
(sqrt (/ 1 x))
(/ 1 x)
1
x
(/ (* (sqrt x) 1/2) x)
(* (sqrt x) 1/2)
(sqrt x)
x
1/2
(/ 1 (/ 1 (- (sqrt (+ 1 x)) (sqrt x))))
1
(/ 1 (- (sqrt (+ 1 x)) (sqrt x)))
(- (sqrt (+ 1 x)) (sqrt x))
(sqrt (+ 1 x))
(+ 1 x)
x
(sqrt x)
(/ 1 (/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))))
1
(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))
x
(+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))
(/ -1/8 (sqrt x))
-1/8
(sqrt x)
(* (sqrt x) 1/2)
1/2

Outputs
(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(/ -1/8 (sqrt x))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
-1/8
#s(literal -1/8 binary64)
(sqrt x)
(sqrt.f64 x)
x
(* (sqrt x) 1/2)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
1/2
#s(literal 1/2 binary64)
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ (* (sqrt x) 1/2) x)
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(* (sqrt x) 1/2)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
x
1/2
#s(literal 1/2 binary64)
(/ 1 (/ 1 (- (sqrt (+ 1 x)) (sqrt x))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1
#s(literal 1 binary64)
(/ 1 (- (sqrt (+ 1 x)) (sqrt x)))
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(- (sqrt (+ 1 x)) (sqrt x))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt (+ 1 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(sqrt x)
(sqrt.f64 x)
(/ 1 (/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))))
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
1
#s(literal 1 binary64)
(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))
(/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
x
(+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))
(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(/ -1/8 (sqrt x))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
-1/8
#s(literal -1/8 binary64)
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) 1/2)
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize340.0ms (3.1%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
✓	accuracy	99.2%	(/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	accuracy	7.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	99.5%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

Results

161.0ms	151×	1	valid
132.0ms	94×	2	valid
4.0ms	11×	0	valid

Compiler

Compiled 150 to 21 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-div: 37.0ms (38% of total)

backward-pass: 23.0ms (23.6% of total)

ival-sqrt: 15.0ms (15.4% of total)

ival-mult: 11.0ms (11.3% of total)

ival-add: 6.0ms (6.2% of total)

ival-sub: 3.0ms (3.1% of total)

const: 1.0ms (1% of total)

series14.0ms (0.1%)

Counts

15 → 180

Calls

Call 1

Inputs
#<alt (/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)>
#<alt (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))>
#<alt (/ -1/8 (sqrt x))>
#<alt (sqrt x)>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ 1 x)>
#<alt (/ (* (sqrt x) 1/2) x)>
#<alt (* (sqrt x) 1/2)>
#<alt (/ 1 (/ 1 (- (sqrt (+ 1 x)) (sqrt x))))>
#<alt (/ 1 (- (sqrt (+ 1 x)) (sqrt x)))>
#<alt (- (sqrt (+ 1 x)) (sqrt x))>
#<alt (sqrt (+ 1 x))>
#<alt (/ 1 (/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))))>
#<alt (/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))>

Outputs
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt (/ 1 (- 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (+ (* -5/32 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))))) (pow x 6))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))))))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (* -8 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* -32 (sqrt x)) (* -8 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* -128 (sqrt x)) (* 32 (sqrt (/ 1 x)))))))>
#<alt (* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* x (- (* -512 (sqrt x)) (* 128 (sqrt (/ 1 x))))) (* 32 (sqrt (/ 1 x)))))))>
#<alt (* 2 (sqrt x))>
#<alt (+ (* 1/2 (sqrt (/ 1 x))) (* 2 (sqrt x)))>
#<alt (- (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt x))) (* -1/2 (sqrt (/ 1 x))))>
#<alt (- (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* -2 (sqrt x))>
#<alt (+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (+ (* -2 (sqrt x)) (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))>
#<alt (+ (* -2 (sqrt x)) (* -1 (/ (- (* -1 (/ (- (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 6)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))>

Calls

45 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
1.0ms	x	@	-inf	(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))
0.0ms	x	@	-inf	(/ -1/8 (sqrt x))
0.0ms	x	@	inf	(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))
0.0ms	x	@	0	(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))

rewrite346.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4174×	`-lowering-.f32`
4174×	`-lowering-.f64`
3898×	`/-lowering-/.f32`
3898×	`/-lowering-/.f64`
1828×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	93
1	123	86
2	942	84
0	8416	84

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 797

Calls

Call 1

Inputs
(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
(+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))
(/ -1/8 (sqrt x))
(sqrt x)
(* 1/2 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ 1 x)
(/ (* (sqrt x) 1/2) x)
(* (sqrt x) 1/2)
(/ 1 (/ 1 (- (sqrt (+ 1 x)) (sqrt x))))
(/ 1 (- (sqrt (+ 1 x)) (sqrt x)))
(- (sqrt (+ 1 x)) (sqrt x))
(sqrt (+ 1 x))
(/ 1 (/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2))))
(/ x (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)))

Outputs
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(-.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
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(/.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/262144 binary64) (.f64 x (.f64 x x))) (pow.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (+.f64 (/.f64 #s(literal 1/4096 binary64) (.f64 x x)) (-.f64 (pow.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))))))
(/.f64 (.f64 x (-.f64 (/.f64 #s(literal 1/4096 binary64) (.f64 x x)) (pow.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (-.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))))
(pow.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1 binary64))
(.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(.f64 x (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(.f64 (sqrt.f64 x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) (/.f64 #s(literal -1 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(*.f64 (/.f64 #s(literal -1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))
(.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) x)
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) #s(literal 1 binary64)) (pow.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))))
(.f64 (/.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) x))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (/.f64 #s(literal -1 binary64) x)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) #s(literal 1 binary64)) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 #s(literal -1/4 binary64) x))) #s(literal -1 binary64)) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (pow.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal 1/2 binary64)))

simplify288.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

4358×	`+-lowering-+.f64`
4358×	`+-lowering-+.f32`
3410×	`-lowering-.f32`
3410×	`-lowering-.f64`
1382×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	1907
1	892	1699
2	3247	1683
0	8250	1683

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/ 1 (- 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (- (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (+ (* -5/32 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))) (* 1/16 (* (sqrt (pow x 5)) (/ 1 (pow (sqrt -1) 4)))))) (pow x 6))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))))))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -8 (sqrt (pow x 3)))
(* (pow x 2) (+ (* -32 (sqrt x)) (* -8 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* -128 (sqrt x)) (* 32 (sqrt (/ 1 x)))))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* x (- (* -512 (sqrt x)) (* 128 (sqrt (/ 1 x))))) (* 32 (sqrt (/ 1 x)))))))
(* 2 (sqrt x))
(+ (* 1/2 (sqrt (/ 1 x))) (* 2 (sqrt x)))
(- (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt x))) (* -1/2 (sqrt (/ 1 x))))
(- (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(* -2 (sqrt x))
(+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* -1 (/ (- (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 6)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))

Outputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* 1/2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
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(* (pow x 2) (+ (* -32 (sqrt x)) (* -8 (sqrt (/ 1 x)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 x) #s(literal -32 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -8 binary64))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* -128 (sqrt x)) (* 32 (sqrt (/ 1 x)))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -8 binary64)) (.f64 x (+.f64 (.f64 (sqrt.f64 x) #s(literal -128 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -32 binary64))))))
(* (pow x 2) (+ (* -8 (sqrt (/ 1 x))) (* x (- (* x (- (* -512 (sqrt x)) (* 128 (sqrt (/ 1 x))))) (* 32 (sqrt (/ 1 x)))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -8 binary64)) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 (sqrt.f64 x) #s(literal -512 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -128 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -32 binary64))))))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(+ (* 1/2 (sqrt (/ 1 x))) (* 2 (sqrt x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(- (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt x))) (* -1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(- (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 x))) (* -1/8 (sqrt (/ 1 (pow x 3))))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/8 binary64)) (+.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/32 binary64)))))
(* -2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal -2 binary64))
(+ (* -2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 x) #s(literal -2 binary64)))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (.f64 (sqrt.f64 x) #s(literal -2 binary64)) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
(+ (* -2 (sqrt x)) (* -1 (/ (- (* -1 (/ (- (* 1/32 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 6)))) (* 1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 4))))) x)) (* 1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(+.f64 (.f64 (sqrt.f64 x) #s(literal -2 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) x) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x))

eval190.0ms (1.7%)

Compiler: Compiled 25286 to 2457 computations (90.3% saved)

prune115.0ms (1%)

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	1283	11	1294
Fresh	4	2	6
Picked	2	3	5
Done	1	2	3
Total	1290	18	1308

Accuracy

100.0%

Counts

1308 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.2%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	5.5%	(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	9.4%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
✓	98.3%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	97.0%	(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
▶	96.7%	(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x)
✓	97.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	90.3%	(/.f64 (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x))) #s(literal 1/2 binary64)) x)
▶	7.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))))
✓	7.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	97.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
▶	98.4%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
▶	97.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.4%	(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
	97.5%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
▶	96.7%	(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)))
	90.3%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 358 to 249 computations (30.4% saved)

simplify152.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))))
✓	cost-diff	0	(pow.f64 x #s(literal -1/4 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)))
✓	cost-diff	6464	(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	192	(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))

Rules

1916×	`-lowering-.f32`
1916×	`-lowering-.f64`
1648×	`div-sub`
1252×	`/-lowering-/.f32`
1252×	`/-lowering-/.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	27	127
1	50	125
2	86	125
3	134	125
4	221	125
5	400	122
6	820	122
7	1971	122
8	2929	122
9	6339	122
10	7955	122
0	8382	122

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize347.0ms (3.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x))))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))
✓	accuracy	7.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)))
✓	accuracy	99.2%	(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x)
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))

Results

155.0ms	151×	1	valid
133.0ms	94×	2	valid
5.0ms	11×	0	valid

Compiler

Compiled 152 to 28 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 142.0ms

ival-div: 32.0ms (22.5% of total)

ival-pow: 28.0ms (19.7% of total)

backward-pass: 27.0ms (19% of total)

ival-mult: 22.0ms (15.5% of total)

ival-sqrt: 16.0ms (11.3% of total)

ival-add: 11.0ms (7.7% of total)

ival-sub: 4.0ms (2.8% of total)

const: 2.0ms (1.4% of total)

series94.0ms (0.8%)

Counts

18 → 216

Calls

Call 1

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

Outputs
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* -8 (sqrt x)) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 2 (sqrt (/ 1 x))) (* x (- (* 32 (sqrt x)) (* 8 (sqrt (/ 1 x)))))))>
#<alt (* x (+ (* 2 (sqrt (/ 1 x))) (* x (- (* x (- (* -128 (sqrt x)) (* -32 (sqrt (/ 1 x))))) (* 8 (sqrt (/ 1 x)))))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/32 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/128 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt x))) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* 1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1/32 (sqrt (/ 1 x))) (* 1/8 (sqrt x))) x)) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/128 (sqrt (/ 1 x))) (* -1/32 (sqrt x))) x)) (* 1/8 (sqrt x))) x)) (* 1/2 (sqrt x))) x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (sqrt x))>
#<alt (* -1/2 (sqrt x))>
#<alt (* -1/2 (sqrt x))>
#<alt (* -1/2 (sqrt x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (pow (/ 1 x) 1/4)>
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))>
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))>
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))>
#<alt (exp (* 1/4 (+ (log -1) (log (/ -1 x)))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -1 (sqrt (/ 1 x))))))>
#<alt (/ 1 (- 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))>
#<alt (/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))))) x))>
#<alt (* -1 (/ (- (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (/ 1 (* (pow (sqrt -1) 4) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/16 (/ (pow x 2) (* (pow (sqrt -1) 4) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))) (* 1/2 (* (sqrt x) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))))) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))))) (pow x 6))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))))))) x))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1 (sqrt (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -1 (sqrt (/ 1 x))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>

Calls

54 calls:

Time	Variable		Point	Expression
33.0ms	x	@	0	(pow x -1/4)
32.0ms	x	@	-inf	(/ 1 (- (sqrt (+ 1 x)) (/ x (sqrt x))))
12.0ms	x	@	-inf	(pow x -1/4)
9.0ms	x	@	inf	(pow x -1/4)
0.0ms	x	@	inf	(/ 1 (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt x) 2)))

rewrite304.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3368×	`/-lowering-/.f32`
3368×	`/-lowering-/.f64`
3190×	`-lowering-.f32`
3190×	`-lowering-.f64`
1852×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	89
1	159	84
2	1104	78
0	8674	78

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1017

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x #s(literal 4 binary64))) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (*.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (*.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (*.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64)))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/4 binary64) x) (+.f64 (.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x #s(literal 4 binary64)))) (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(+.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
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(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))) (.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64)))) (pow.f64 x #s(literal 3/2 binary64)))) (*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64)))) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))))
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(/.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
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(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x))) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (+.f64 (.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))))
(pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(*.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)))
(*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))))
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal -1/2 binary64))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64)))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (.f64 (.f64 #s(literal -1/4 binary64) (log.f64 x)) #s(literal -2 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(sqrt.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(/.f64 x (sqrt.f64 x))
(/.f64 (sqrt.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (sqrt.f64 x))
(/.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal -4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 x (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) x)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 x (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -3/8 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/8 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 x (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))

simplify256.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

3792×	`+-lowering-+.f64`
3792×	`+-lowering-+.f32`
3190×	`-lowering-.f32`
3190×	`-lowering-.f64`
1156×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	2176
1	919	1810
2	3107	1657
0	8933	1657

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* 2 (sqrt x))
(* x (+ (* -8 (sqrt x)) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* 2 (sqrt (/ 1 x))) (* x (- (* 32 (sqrt x)) (* 8 (sqrt (/ 1 x)))))))
(* x (+ (* 2 (sqrt (/ 1 x))) (* x (- (* x (- (* -128 (sqrt x)) (* -32 (sqrt (/ 1 x))))) (* 8 (sqrt (/ 1 x)))))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/32 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/128 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt x))) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
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(* -1 (/ (+ (* -1 (/ (- (* -1/32 (sqrt (/ 1 x))) (* 1/8 (sqrt x))) x)) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (* 1/128 (sqrt (/ 1 x))) (* -1/32 (sqrt x))) x)) (* 1/8 (sqrt x))) x)) (* 1/2 (sqrt x))) x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)
(/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)
(/ (+ (* 1/2 (sqrt x)) (* 2 (sqrt (pow x 3)))) x)
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* -1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (sqrt x))
(* -1/2 (sqrt x))
(* -1/2 (sqrt x))
(* -1/2 (sqrt x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(pow (/ 1 x) 1/4)
(exp (* 1/4 (+ (log -1) (log (/ -1 x)))))
(exp (* 1/4 (+ (log -1) (log (/ -1 x)))))
(exp (* 1/4 (+ (log -1) (log (/ -1 x)))))
(exp (* 1/4 (+ (log -1) (log (/ -1 x)))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -1 (sqrt (/ 1 x))))))
(/ 1 (- 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (- (+ (* -1 (/ (+ (* -5/32 (sqrt (pow x 5))) (+ (* 1/16 (sqrt (pow x 5))) (* 1/4 (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))))))) (pow x 6))) (* 2 (sqrt (/ 1 x)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 5))))))))
(/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))))) x))
(* -1 (/ (- (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/16 (* (sqrt (pow x 5)) (/ 1 (* (pow (sqrt -1) 4) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/16 (/ (pow x 2) (* (pow (sqrt -1) 4) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))) (* 1/2 (* (sqrt x) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))))) (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))))) (pow x 6))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x)))) 3)))))))) x))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* -1 (sqrt (/ 1 x))))))
(* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -1 (sqrt (/ 1 x))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)

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

eval157.0ms (1.4%)

Compiler: Compiled 22115 to 2956 computations (86.6% saved)

prune149.0ms (1.3%)

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	1336	9	1345
Fresh	6	2	8
Picked	4	1	5
Done	1	4	5
Total	1347	16	1363

Accuracy

100.0%

Counts

1363 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64))))
	96.7%	(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) x)
	96.7%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
✓	6.2%	(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	5.5%	(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
	9.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	97.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	98.6%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
	97.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
	98.2%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))))
	97.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
✓	7.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	97.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.5%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	3.8%	(*.f64 x #s(literal 0 binary64))

Compiler

Compiled 670 to 275 computations (59% saved)

regimes26.0ms (0.2%)

Counts

39 → 1

Calls

Call 1

Inputs
(*.f64 x #s(literal 0 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) x)
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1/4 binary64)) (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))))
(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) x) (*.f64 x #s(literal 4 binary64))) (/.f64 (-.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x))) #s(literal 1/2 binary64)) x)
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x) x)
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (+.f64 (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))) (+.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 3/2 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))))

Outputs

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

Calls

2 calls:

14.0ms	x
9.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
97.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

13 → 1

Calls

Call 1

Inputs
(*.f64 x #s(literal 0 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) x)
(/.f64 (*.f64 (/.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))

Outputs
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
97.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 x #s(literal 0 binary64))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -1.4b remaining (-2.3%)

Threshold costs -1.4b (-2.3%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 x #s(literal 0 binary64))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
3.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

66×	`neg-mul-1_binary64`
62×	`unsub-neg_binary64`
32×	`*-commutative_binary64`
28×	`+-commutative_binary64`
26×	`sub-neg_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	28	70
1	44	70
2	62	70
3	80	70
4	94	70
5	109	70
6	121	69
7	129	69
8	173	69
9	243	69

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.2s (20.2%)

Rules

4358×	`+-lowering-+.f64`
4358×	`+-lowering-+.f32`
4174×	`-lowering-.f32`
4174×	`-lowering-.f64`
3898×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	278	1907
1	892	1699
2	3247	1683
0	8250	1683
0	295	2176
1	919	1810
2	3107	1657
0	8933	1657
0	39	123
1	293	115
2	2770	113
0	9047	113
0	113	434
1	325	384
2	1039	376
3	3226	373
4	7122	373
0	8132	373
0	27	89
1	159	84
2	1104	78
0	8674	78
0	6	16
1	39	16
2	303	16
3	3722	16
0	8049	16
0	20	93
1	123	86
2	942	84
0	8416	84

Stop Event

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

Compiler

Compiled 333 to 229 computations (31.2% saved)

preprocess49.0ms (0.4%)

Compiler: Compiled 176 to 82 computations (53.4% saved)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

analyze3.0ms (0%)

sample2.6s (23.5%)

preprocess52.0ms (0.5%)

explain233.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

localize76.0ms (0.7%)

series4.0ms (0%)

rewrite335.0ms (3%)

simplify224.0ms (2%)

eval72.0ms (0.6%)

prune45.0ms (0.4%)

simplify255.0ms (2.3%)

localize700.0ms (6.3%)

series38.0ms (0.3%)

rewrite343.0ms (3.1%)

simplify380.0ms (3.4%)

eval251.0ms (2.3%)

prune205.0ms (1.8%)

simplify146.0ms (1.3%)

localize340.0ms (3.1%)

series14.0ms (0.1%)

rewrite346.0ms (3.1%)

simplify288.0ms (2.6%)

eval190.0ms (1.7%)

prune115.0ms (1%)

simplify152.0ms (1.4%)

localize347.0ms (3.1%)

series94.0ms (0.8%)

rewrite304.0ms (2.7%)

simplify256.0ms (2.3%)

eval157.0ms (1.4%)

prune149.0ms (1.3%)

regimes26.0ms (0.2%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify13.0ms (0.1%)

soundness2.2s (20.2%)

preprocess49.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18