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)

sample1.9s (21.5%)

Results

812.0ms	4786×	1	valid
768.0ms	3269×	2	valid
16.0ms	201×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sqrt: 311.0ms (29.2% of total)

backward-pass: 205.0ms (19.2% of total)

...c/correct-round.rkt:119:19: 143.0ms (13.4% of total)

ival-add: 137.0ms (12.9% of total)

ival-sub: 116.0ms (10.9% of total)

ival->: 76.0ms (7.1% of total)

ival-and: 35.0ms (3.3% of total)

ival-<: 26.0ms (2.4% of total)

const: 18.0ms (1.7% of total)

Bogosity

preprocess43.0ms (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)))

explain151.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
254	1	(99.30215825495974)	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	0	-	-	`x`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`

Results

59.0ms	212×	2	valid
53.0ms	292×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-sqrt: 18.0ms (33.8% of total)

backward-pass: 17.0ms (31.9% of total)

ival-add: 10.0ms (18.8% of total)

ival-sub: 6.0ms (11.3% of total)

const: 1.0ms (1.9% 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
▶	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify15.0ms (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)

localize97.0ms (1.1%)

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	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

59.0ms	106×	2	valid
27.0ms	146×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sqrt: 11.0ms (38.7% of total)

backward-pass: 8.0ms (28.2% of total)

ival-add: 5.0ms (17.6% of total)

ival-sub: 4.0ms (14.1% of total)

const: 1.0ms (3.5% of total)

series5.0ms (0.1%)

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)

rewrite720.0ms (8%)

Algorithm

1×	batch-egg-rewrite

Rules

2006×	`-lowering-.f32`
2006×	`-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	3743	16
0	8181	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 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))))))
(fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (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 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (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 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (/.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 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) #s(literal 3 binary64)))) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (.f64 (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) (-.f64 (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) (+.f64 x #s(literal 1 binary64))))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 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 (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))) (-.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))))))
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(/.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 (.f64 (pow.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x x)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 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 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.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)))

simplify237.0ms (2.6%)

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	332	384
2	1042	376
3	3238	373
4	7124	373
0	8133	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 #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 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.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))))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (sqrt.f64 x)))
(* 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 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.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 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 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 #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 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 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (-.f64 (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 1/8 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 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)

eval34.0ms (0.4%)

Compiler: Compiled 5895 to 845 computations (85.7% saved)

prune41.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	262	6	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	262	7	269

Accuracy

99.9%

Counts

269 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	3.3%	(/.f64 (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 x (.f64 x x))) (.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 x (+.f64 x (+.f64 x #s(literal 1 binary64)))))))
▶	99.2%	(/.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)
▶	98.9%	(/.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)
▶	7.6%	(/.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)))
✓	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	98.4%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 244 to 152 computations (37.7% saved)

simplify190.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2262×	`fnmsub-define`
2040×	`sum5-define`
1354×	`sum3-define`
1324×	`sum4-define`
1048×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	240
1	74	237
2	135	233
3	256	232
4	363	232
5	426	232
6	552	232
7	740	232
8	1061	232
9	1784	232
10	4157	232
11	6767	232
0	8117	232

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize411.0ms (4.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	99.7%	(/.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)))
✓	accuracy	6.9%	(+.f64 x (-.f64 #s(literal 1 binary64) 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	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.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)
✓	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	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))
✓	accuracy	99.1%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	79.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))
✓	accuracy	66.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Results

308.0ms	240×	1	valid
8.0ms	16×	0	valid

Compiler

Compiled 300 to 36 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 158.0ms

backward-pass: 42.0ms (26.6% of total)

ival-mult: 29.0ms (18.3% of total)

ival-div: 25.0ms (15.8% of total)

ival-pow: 20.0ms (12.6% of total)

ival-add: 19.0ms (12% of total)

ival-sqrt: 14.0ms (8.9% of total)

ival-sub: 8.0ms (5.1% of total)

const: 2.0ms (1.3% of total)

series22.0ms (0.2%)

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) (* -5/128 (sqrt (/ 1 (pow x 5)))))) x)>
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (+ (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) (* -5/128 (sqrt (/ 1 (pow x 5))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (- 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ 1 x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)>
#<alt (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2))>
#<alt (+ x (- 1 x))>
#<alt (/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))>
#<alt (- 1 x)>
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))>
#<alt (sqrt (/ 1 (* x (* x x))))>
#<alt (sqrt (/ 1 (pow x 5)))>
#<alt (/ 1 (* x (* x x)))>
#<alt (/ 1 (pow x 5))>

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

Calls

54 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) (* -5/128 (sqrt (/ 1 (pow x 5)))))) x)
2.0ms	x	@	0	(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (pow (+ x 1) 1/2) (sqrt x)))
1.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) (* -5/128 (sqrt (/ 1 (pow x 5)))))) x)
1.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (+ (* (sqrt x) 1/2) (* 1/16 (sqrt (/ 1 (* x (* x x)))))) (* -5/128 (sqrt (/ 1 (pow x 5)))))) x)

rewrite390.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3364×	`-lowering-.f32`
3364×	`-lowering-.f64`
2722×	`fma-lowering-fma.f32`
2722×	`fma-lowering-fma.f64`
2376×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	133
1	231	109
2	2076	108
0	9101	108

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 533

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))) #s(literal 1 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 3 binary64))) (.f64 x (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 2 binary64))) (.f64 x (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (.f64 #s(literal -1/8 binary64) (pow.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))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (.f64 #s(literal -1/8 binary64) (pow.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)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) x))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64)))))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 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))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))
(pow.f64 (/.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 5/2 binary64))))))) #s(literal -1 binary64))
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(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.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)) (sqrt.f64 x))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(.f64 (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))))
(exp.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(fabs.f64 (pow.f64 x #s(literal -3/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) x)
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(pow.f64 x #s(literal -3/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -3 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 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) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -5/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 5 binary64) (log.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 5/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 5/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal 5/2 binary64))))
(fabs.f64 (pow.f64 x #s(literal -5/2 binary64)))
(sqrt.f64 (pow.f64 x #s(literal -5 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 x #s(literal 5/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 5/2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 x #s(literal -5/2 binary64))) (pow.f64 x #s(literal 5/4 binary64)))
(pow.f64 x #s(literal -5/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -5 binary64))
(pow.f64 (*.f64 x x) #s(literal -5/4 binary64))
(pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -5/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal -5 binary64)) (pow.f64 x #s(literal -5 binary64))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -5/2 binary64)))
(*.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -5/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))))
(*.f64 (pow.f64 x #s(literal -5/4 binary64)) (pow.f64 x #s(literal -5/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -5/2 binary64)) (pow.f64 x #s(literal -5/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -5/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -5/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 5/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -5/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -5/2 binary64))))
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(pow.f64 x #s(literal -3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal -5 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (.f64 (.f64 (log.f64 x) #s(literal -5 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 5/2 binary64))))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal -5 binary64)) (pow.f64 x #s(literal -5 binary64))))
(sqrt.f64 (/.f64 (pow.f64 x #s(literal -5 binary64)) (pow.f64 x #s(literal 5 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64)))))
(/.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal 5/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64))))
(pow.f64 x #s(literal -5 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -10 binary64))
(pow.f64 (*.f64 x x) #s(literal -5/2 binary64))
(pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -5/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 5 binary64))) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal -5 binary64)) (pow.f64 x #s(literal -5 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -5 binary64)))
(*.f64 (pow.f64 x #s(literal -5 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -5/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 5 binary64)))))

simplify282.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

3820×	`-lowering-.f32`
3820×	`-lowering-.f64`
2258×	`+-lowering-+.f64`
2258×	`+-lowering-+.f32`
1152×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	1966
1	811	1661
2	2979	1638
3	7520	1638
0	8030	1638

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval164.0ms (1.8%)

Compiler: Compiled 26790 to 2785 computations (89.6% saved)

prune102.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	972	8	980
Fresh	1	0	1
Picked	5	0	5
Done	0	1	1
Total	978	9	987

Accuracy

100.0%

Counts

987 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	22.6%	(/.f64 (/.f64 (+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 x (.f64 x x))) x)
▶	98.9%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	7.6%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
▶	98.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	98.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.5%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	90.9%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 212 to 144 computations (32.1% saved)

simplify39.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -5/128 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 x (.f64 x x)))
✓	cost-diff	0	(/.f64 (/.f64 (+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 x (.f64 x x))) x)
✓	cost-diff	6400	(+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))
✓	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)
✓	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	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(+.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)))

Rules

712×	`fma-define`
644×	`fma-lowering-fma.f32`
644×	`fma-lowering-fma.f64`
220×	`-lowering-.f32`
220×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	239
1	75	230
2	172	225
3	354	222
4	595	222
5	799	222
6	872	222
7	875	222
0	875	222

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize239.0ms (2.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 #s(literal -5/128 binary64) (sqrt.f64 x))
✓	accuracy	72.0%	(+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))
✓	accuracy	66.5%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	26.0%	(/.f64 (+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 x (.f64 x 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	99.7%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) 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%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))

Results

137.0ms

256×

valid

Compiler

Compiled 274 to 32 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-div: 19.0ms (34.6% of total)

ival-mult: 16.0ms (29.2% of total)

ival-add: 8.0ms (14.6% of total)

ival-pow: 6.0ms (10.9% of total)

ival-sqrt: 4.0ms (7.3% of total)

const: 1.0ms (1.8% of total)

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

series9.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (/ 1 (+ (pow (+ x 1) 1/2) (sqrt x)))>
#<alt (+ (pow (+ x 1) 1/2) (sqrt x))>
#<alt (pow (+ x 1) 1/2)>
#<alt (+ x 1)>
#<alt (/ 1/2 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ (* (sqrt x) 1/2) x)>
#<alt (* (sqrt x) 1/2)>
#<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 (+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8))))))>
#<alt (/ (/ (+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))))) (* x (* x x))) x)>
#<alt (/ (+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))))) (* x (* x x)))>
#<alt (* -5/128 (sqrt x))>
#<alt (sqrt (* x (* x x)))>
#<alt (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8))))>

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

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ 1/2 (sqrt x))
1.0ms	x	@	-inf	(+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8))))))
1.0ms	x	@	-inf	(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
0.0ms	x	@	-inf	(/ (+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8)))))) (* x (* x x)))
0.0ms	x	@	inf	(+ (* -5/128 (sqrt x)) (* x (+ (* (sqrt (* x (* x x))) (* x 1/2)) (* (sqrt x) (+ 1/16 (* x -1/8))))))

rewrite379.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2666×	`-lowering-.f32`
2666×	`-lowering-.f64`
2556×	`fma-lowering-fma.f32`
2556×	`fma-lowering-fma.f64`
2272×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	160
1	206	149
2	1827	139
0	8361	139

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 507

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(*.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))) (/.f64 x (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
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(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))))
(+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))
(+.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))))
(+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (/.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))
(-.f64 (/.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))
(fma.f64 (sqrt.f64 x) #s(literal 1/16 binary64) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))))
(fma.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))
(fma.f64 (sqrt.f64 x) (.f64 x (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 x #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(fma.f64 #s(literal 1/16 binary64) (sqrt.f64 x) (+.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))
(fma.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))
(fma.f64 (.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) x (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))
(fma.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x)) x (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))))))
(/.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))) (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))
(/.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))) (+.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))))
(/.f64 (-.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))))) (neg.f64 (-.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))))))
(pow.f64 (/.f64 (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 (pow.f64 x #s(literal 9/2 binary64)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64))) (pow.f64 (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (sqrt.f64 x)) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))) (.f64 x (.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))))))

simplify314.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

3862×	`+-lowering-+.f64`
3862×	`+-lowering-+.f32`
3806×	`-lowering-.f32`
3806×	`-lowering-.f64`
1114×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	297	2354
1	983	2051
2	3898	2024
0	8177	2024

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

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

eval159.0ms (1.8%)

Compiler: Compiled 21048 to 2287 computations (89.1% saved)

prune182.0ms (2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	888	5	893
Fresh	2	1	3
Picked	2	3	5
Done	0	1	1
Total	892	10	902

Accuracy

100.0%

Counts

902 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.6%	(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -5/128 binary64)) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) x) x) x) x)
✓	98.9%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	98.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 x))))
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	98.0%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	98.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	90.9%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	98.5%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Compiler

Compiled 180 to 127 computations (29.4% saved)

simplify148.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (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)) (/.f64 x (sqrt.f64 x))))
✓	cost-diff	64	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	128	(/.f64 x (sqrt.f64 x))
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (log.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	cost-diff	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	cost-diff	128	(/.f64 x (sqrt.f64 x))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	64	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	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)))

Rules

2068×	`fnmadd-define`
1518×	`fma-lowering-fma.f32`
1518×	`fma-lowering-fma.f64`
1384×	`fmsub-define`
1308×	`fmm-def`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	21	92
1	41	92
2	48	92
3	55	92
4	60	92
5	75	92
6	93	89
7	193	88
8	1175	88
9	3791	88
10	6756	88
0	8078	88

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize160.0ms (1.8%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 x)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 x))))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 x))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	accuracy	92.2%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Results

131.0ms

256×

valid

Compiler

Compiled 113 to 22 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-pow: 11.0ms (25.4% of total)

ival-div: 8.0ms (18.5% of total)

ival-mult: 8.0ms (18.5% of total)

ival-add: 6.0ms (13.9% of total)

ival-sqrt: 4.0ms (9.2% of total)

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

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

const: 1.0ms (2.3% of total)

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

series75.0ms (0.8%)

Counts

16 → 192

Calls

Call 1

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

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

Calls

48 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	(* 1/2 (log x))
16.0ms	x	@	inf	(* 1/2 (log x))
12.0ms	x	@	-inf	(* 1/2 (log x))
5.0ms	x	@	0	(+ (sqrt (+ 1 x)) (sqrt x))
2.0ms	x	@	-inf	(/ 1 (+ (pow (+ x 1) 1/2) (/ x (sqrt x))))

rewrite251.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2754×	`-lowering-.f32`
2754×	`-lowering-.f64`
2704×	`/-lowering-/.f32`
2704×	`/-lowering-/.f64`
1280×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	77
1	141	73
2	937	66
0	9154	66

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 642

Calls

Call 1

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

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

simplify291.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3874×	`+-lowering-+.f64`
3874×	`+-lowering-+.f32`
3818×	`-lowering-.f32`
3818×	`-lowering-.f64`
1274×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	2144
1	866	1780
2	3208	1766
0	8298	1766

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval121.0ms (1.3%)

Compiler: Compiled 16187 to 1938 computations (88% saved)

prune140.0ms (1.5%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	997	2	999
Fresh	0	1	1
Picked	1	4	5
Done	0	4	4
Total	998	11	1009

Accuracy

100.0%

Counts

1009 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	23.6%	(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -5/128 binary64)) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) x) x) x) x)
✓	98.9%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	98.1%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 x (sqrt.f64 x))))
✓	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	98.0%	(/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x)))
	98.0%	(/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
✓	98.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	90.9%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	6.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	98.5%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Compiler

Compiled 414 to 186 computations (55.1% saved)

regimes13.0ms (0.1%)

Counts

22 → 1

Calls

Call 1

Inputs
(-.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 1/2 binary64) (/.f64 x (sqrt.f64 x)))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 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 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 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)
(/.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 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (.f64 x (.f64 x x))) (.f64 (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)) (+.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (*.f64 x (+.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (/.f64 (/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -5/128 binary64)) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal -1/8 binary64))))))) x) x) x) x)
(/.f64 (/.f64 (+.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 x)) (.f64 x (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))))) (.f64 x (.f64 x 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)

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

Calls

2 calls:

6.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes9.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.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
98.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
1.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	21	22
2	25	22
3	27	22
4	28	22

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.6s (17.6%)

Rules

3820×	`-lowering-.f32`
3820×	`-lowering-.f64`
3364×	`-lowering-.f32`
3364×	`-lowering-.f64`
2970×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	160
1	206	149
2	1827	139
0	8361	139
0	113	434
1	332	384
2	1042	376
3	3238	373
4	7124	373
0	8133	373
0	35	133
1	231	109
2	2076	108
0	9101	108
0	6	16
1	39	16
2	303	16
3	3743	16
0	8181	16
0	260	1966
1	811	1661
2	2979	1638
3	7520	1638
0	8030	1638

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

Compiler

Compiled 89 to 63 computations (29.2% saved)

preprocess48.0ms (0.5%)

Compiler: Compiled 82 to 52 computations (36.6% 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	31	239
1	75	230
2	172	225
3	354	222
4	595	222
5	799	222
6	872	222
7	875	222
0	875	222

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	31	239
1	75	230
2	172	225
3	354	222
4	595	222
5	799	222
6	872	222
7	875	222
0	875	222

analyze3.0ms (0%)

sample1.9s (21.5%)

preprocess43.0ms (0.5%)

explain151.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize97.0ms (1.1%)

series5.0ms (0.1%)

rewrite720.0ms (8%)

simplify237.0ms (2.6%)

eval34.0ms (0.4%)

prune41.0ms (0.5%)

simplify190.0ms (2.1%)

localize411.0ms (4.6%)

series22.0ms (0.2%)

rewrite390.0ms (4.3%)

simplify282.0ms (3.1%)

eval164.0ms (1.8%)

prune102.0ms (1.1%)

simplify39.0ms (0.4%)

localize239.0ms (2.6%)

series9.0ms (0.1%)

rewrite379.0ms (4.2%)

simplify314.0ms (3.5%)

eval159.0ms (1.8%)

prune182.0ms (2%)

simplify148.0ms (1.6%)

localize160.0ms (1.8%)

series75.0ms (0.8%)

rewrite251.0ms (2.8%)

simplify291.0ms (3.2%)

eval121.0ms (1.3%)

prune140.0ms (1.5%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify8.0ms (0.1%)

soundness1.6s (17.6%)

preprocess48.0ms (0.5%)

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

Iter	Nodes	Cost
0	31	239
1	75	230
2	172	225
3	354	222
4	595	222
5	799	222
6	872	222
7	875	222
0	875	222