Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

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 19 to 13 computations (31.6% saved)

sample2.1s (24.1%)

Memory

-116.2MiB live, 2 393.2MiB allocated

Samples

1.4s	6 877×	1	valid
248.0ms	1 096×	2	valid
24.0ms	283×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

adjust: 429.0ms (31.6% of total)

ival-div: 295.0ms (21.7% of total)

ival-sqrt: 276.0ms (20.3% of total)

const: 127.0ms (9.3% of total)

ival-sub: 81.0ms (6% of total)

ival-add: 80.0ms (5.9% of total)

ival->: 29.0ms (2.1% of total)

ival-<: 19.0ms (1.4% of total)

ival-and: 12.0ms (0.9% of total)

exact: 8.0ms (0.6% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain182.0ms (2.1%)

Memory

-9.8MiB live, 160.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
181	1	(1.4215915075738818e+215)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`	cancellation	182	3

Confusion

	Predicted +	Predicted -
+	181	1
-	1	73

Precision

0.9945054945054945

Recall

0.9945054945054945

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	181	1	0
-	1	2	71

Precision?

0.9837837837837838

Recall?

1.0

Freqs

test

number	freq
0	74
1	182

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

60.0ms	448×	1	valid
8.0ms	38×	2	valid
2.0ms	26×	0	valid

Compiler

Compiled 79 to 28 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 15.0ms (30.5% of total)

ival-div: 13.0ms (26.4% of total)

adjust: 10.0ms (20.3% of total)

ival-add: 5.0ms (10.2% of total)

ival-sub: 5.0ms (10.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess21.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	20	25
2	47	24
3	89	24
4	144	24
5	209	24
6	245	24
7	272	24
8	281	24
0	8	11
0	14	11
1	19	11
2	27	11
3	36	11
4	48	11
5	68	11
6	107	11
7	139	11
8	195	11
9	224	11
10	245	11
11	247	11
0	247	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify8.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	32
0	14	32
1	19	32
2	27	32
3	36	32
4	48	32
5	68	32
6	107	32
7	139	32
8	195	32
9	224	32
10	245	32
11	247	32
0	247	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (0.6%)

Memory

-14.0MiB live, 66.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.25	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	39.792876907803986	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

31.0ms	224×	1	valid
8.0ms	19×	2	valid
1.0ms	13×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-div: 9.0ms (30.9% of total)

adjust: 8.0ms (27.5% of total)

ival-sqrt: 7.0ms (24.1% of total)

ival-add: 2.0ms (6.9% of total)

ival-sub: 2.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 3/8 x) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2)) (taylor inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	0	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify203.0ms (2.4%)

Memory

0.1MiB live, 226.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	926	455
3	3322	445
0	8129	416

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite147.0ms (1.7%)

Memory

11.3MiB live, 134.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19

Stop Event

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

Counts

4 → 238

Calls

Call 1

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

Outputs
#<batchref>
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eval85.0ms (1%)

Memory: -21.8MiB live, 103.0MiB allocated
Compiler: Compiled 6 175 to 734 computations (88.1% saved)

prune30.0ms (0.4%)

Memory

-7.1MiB live, 32.5MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	273	13	286
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	273	14	287

Accuracy

86.0%

Counts

287 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.5%	(fma.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))) (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))))))
	37.8%	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
▶	37.8%	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.5%	(/.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	40.4%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
	40.4%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓	37.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	27.6%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	32.4%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	37.6%	(*.f64 (+.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (-.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
▶	82.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)))
▶	82.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	60.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
▶	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 513 to 316 computations (38.4% saved)

simplify118.0ms (1.4%)

Memory

14.1MiB live, 132.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)))
cost-diff	128	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
cost-diff	320	(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	768	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff	640	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
cost-diff	832	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
cost-diff	0	(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	359
0	73	361
1	126	359
2	308	341
3	1035	335
4	3987	335
0	8337	333

Stop Event

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

Calls

Call 1

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

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

localize191.0ms (2.2%)

Memory

10.8MiB live, 288.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.625645999908307	(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	1.2349995942849412	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)))
accuracy	10.144214021798227	(/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x))
accuracy	22.272335412479443	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
accuracy	0.18359375	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
accuracy	0.24609375	(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.515625	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
accuracy	57.170917204144864	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.209316259768442	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.3671875	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	58.47460252681937	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.3030830512408	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.10546875	(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	2.1264032377448414	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
accuracy	9.077439016909363	(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Samples

135.0ms	224×	1	valid
13.0ms	19×	2	valid
5.0ms	13×	0	valid

Compiler

Compiled 326 to 41 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-div: 27.0ms (26.5% of total)

ival-mult: 23.0ms (22.5% of total)

adjust: 17.0ms (16.7% of total)

ival-sqrt: 11.0ms (10.8% of total)

ival-sub: 10.0ms (9.8% of total)

ival-add: 8.0ms (7.8% of total)

ival-pow: 3.0ms (2.9% of total)

ival-neg: 2.0ms (2% of total)

exact: 1.0ms (1% of total)

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

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

series134.0ms (1.6%)

Memory

-4.1MiB live, 33.2MiB allocated

Counts

23 → 276

Calls

Call 1

Inputs
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (patch (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (patch (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))) (patch (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)) (patch (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sqrt (/ 1 (pow x 5)))) (taylor 0 x) (#s(alt (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (patch (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3)) (taylor 0 x) (#s(alt (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (patch (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3)) (taylor 0 x) (#s(alt (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (patch (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3)) (taylor 0 x) (#s(alt (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (patch (.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (patch (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal -1/2 binary64) x) (patch (/.f64 #s(literal -1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (- 1 (sqrt x))) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (* -1/8 (sqrt x)))))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))) (+ (* -1/8 (sqrt x)) (* x (+ (* -1/4 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (- 1 (sqrt x)))))))))))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (- 1 (sqrt x))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (- 1 (sqrt x)))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- 1 (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* 1/2 x)) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
106.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))
10.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))
6.0ms	x	@	0	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))

Time

Variable

Point

Expression

106.0ms

inf

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))

10.0ms

-inf

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))

6.0ms

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (/ (/ -1/2 x) x) (- (sqrt (/ 1 x)) (sqrt x))) (/ (/ -1/2 x) x) (/ -1/2 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))) (sqrt x) (/ -1 (sqrt (+ x 1))) (sqrt (/ 1 (pow x 3))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/ 1 (pow x 3)))

simplify273.0ms (3.2%)

Memory

15.2MiB live, 240.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	510	4444
1	1500	3714
2	4760	3650
0	8871	3437

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

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

rewrite195.0ms (2.3%)

Memory

-22.6MiB live, 343.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	274
0	73	253
1	302	217
2	2644	217
0	8392	217

Stop Event

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

Counts

23 → 1 010

Calls

Call 1

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

Outputs
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eval623.0ms (7.3%)

Memory: 16.1MiB live, 334.2MiB allocated
Compiler: Compiled 45 195 to 5 636 computations (87.5% saved)

prune226.0ms (2.6%)

Memory

-0.2MiB live, 117.4MiB allocated

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	1 719	25	1 744
Fresh	7	1	8
Picked	4	1	5
Done	1	0	1
Total	1 731	27	1 758

Accuracy

100.0%

Counts

1 758 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.4%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.5%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.5%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)))
	9.4%	(/.f64 (/.f64 (-.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.5%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
	37.8%	(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	37.8%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
	37.9%	(/.f64 (+.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
▶	99.2%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
▶	40.5%	(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.4%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	97.9%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	96.4%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	96.0%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
▶	32.4%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	80.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x #s(literal -2 binary64)) x)))
	96.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) x)) x))
	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
	80.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
▶	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	96.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
	80.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	96.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)))
	34.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
✓	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
	96.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (*.f64 (fma.f64 (/.f64 #s(literal 5/4 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 805 to 531 computations (34% saved)

simplify116.0ms (1.4%)

Memory

-0.5MiB live, 81.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	128	(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	320	(*.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x))
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	640	(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff	0	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
cost-diff	128	(*.f64 (+.f64 x #s(literal 1 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	#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	192	(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	768	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
cost-diff	1280	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	277
0	63	268
1	112	268
2	282	248
3	923	239
4	3089	239
5	5781	239
0	8200	232

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (+ x 1) x) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 x)
(neg.f64 (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x))
#s(literal -1 binary64)
(-.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 x)

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

localize181.0ms (2.1%)

Memory

1.7MiB live, 280.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)
accuracy	0.203125	(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.7107280857254712	(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	57.170917204144864	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.00390625	(*.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.1953125	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
accuracy	27.502523092534357	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
accuracy	58.47460252681937	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0	#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.13671875	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	39.792876907803986	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	0	(sqrt.f64 x)
accuracy	0.25	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.3030830512408	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.02734375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.18359375	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
accuracy	0.24609375	(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.515625	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))

Samples

124.0ms	224×	1	valid
11.0ms	19×	2	valid
3.0ms	13×	0	valid

Compiler

Compiled 262 to 30 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-mult: 23.0ms (23.1% of total)

ival-add: 21.0ms (21% of total)

ival-div: 21.0ms (21% of total)

ival-sqrt: 12.0ms (12% of total)

adjust: 11.0ms (11% of total)

ival-sub: 6.0ms (6% of total)

ival-neg: 4.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.3%)

Memory

10.1MiB live, 47.9MiB allocated

Counts

24 → 288

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x))) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x) (patch (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt x) (+ 1 (sqrt x)))) (* -1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt x) (+ 1 (sqrt x)))) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt (pow x 3)))))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt x) (+ 1 (sqrt x)))) (* x (+ (* -1/2 (sqrt x)) (* x (+ (* -1/16 (sqrt (pow x 3))) (* 1/8 (sqrt x))))))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 x) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* -3/8 x))) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* x (- (* 5/16 x) 3/8)))) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (- 1 (sqrt x))) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x))) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x) (patch (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

-inf

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

3.0ms

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

2.0ms

inf

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

simplify175.0ms (2.1%)

Memory

17.1MiB live, 242.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	681	4600
1	2082	3717
2	7599	3710
0	8368	3470

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 286

Calls

Call 1

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

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

rewrite194.0ms (2.3%)

Memory

-1.3MiB live, 279.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	223
0	63	221
1	241	196
2	1900	196
0	8748	183

Stop Event

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

Counts

24 → 1 034

Calls

Call 1

Inputs
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (+ x 1) x) #s(literal 1 binary64))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (+.f64 x #s(literal 1 binary64)) x)
(*.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)

Outputs
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eval249.0ms (2.9%)

Memory: 39.5MiB live, 455.5MiB allocated
Compiler: Compiled 40 006 to 4 948 computations (87.6% saved)

prune58.0ms (0.7%)

Memory

-22.8MiB live, 177.8MiB allocated

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	1 680	8	1 688
Fresh	8	13	21
Picked	3	2	5
Done	0	1	1
Total	1 691	24	1 715

Accuracy

100.0%

Counts

1 715 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 x)))
	40.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
	9.4%	(/.f64 (/.f64 (-.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	40.5%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
▶	37.8%	(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	37.8%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	37.9%	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
▶	99.6%	(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
▶	96.4%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
	37.2%	(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 #s(approx (+ (* (sqrt (+ x 1)) (sqrt x)) x) (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	97.9%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	96.4%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	98.7%	(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	32.4%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	80.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x #s(literal -2 binary64)) x)))
▶	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
	80.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	80.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	96.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)))
	34.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
✓	5.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
	96.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (*.f64 (fma.f64 (/.f64 #s(literal 5/4 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 628 to 445 computations (29.1% saved)

simplify143.0ms (1.7%)

Memory

-39.1MiB live, 104.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	128	(*.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(/.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x))
cost-diff	0	(-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
cost-diff	192	(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 (sqrt.f64 x) x)
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	128	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))
cost-diff	192	(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	768	(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	304
0	70	300
1	120	300
2	210	268
3	419	266
4	828	264
5	2243	263
6	5085	263
7	7432	263
0	8084	252

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (+ x 1) x) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(neg.f64 x)
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (+ x 1) x) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(literal -1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x))
(/.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
(-.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 x)

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

localize198.0ms (2.3%)

Memory

46.4MiB live, 239.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.21875	(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
accuracy	0.7107280857254712	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
accuracy	27.502523092534357	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
accuracy	57.170917204144864	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.01171875	(sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x))
accuracy	0.209316259768442	(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	57.570560770468724	(-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64))
accuracy	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
accuracy	0.18359375	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
accuracy	0.24609375	(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	2.10945654601762	#s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.2734375	(/.f64 (sqrt.f64 x) x)
accuracy	60.3030830512408	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
accuracy	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
accuracy	0.1015625	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))
accuracy	0.18359375	(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
accuracy	0.24609375	(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))

Samples

93.0ms	157×	1	valid
67.0ms	86×	2	valid
3.0ms	13×	0	valid

Compiler

Compiled 283 to 36 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-div: 36.0ms (32.2% of total)

ival-mult: 19.0ms (17% of total)

adjust: 17.0ms (15.2% of total)

ival-sqrt: 17.0ms (15.2% of total)

ival-add: 12.0ms (10.7% of total)

ival-sub: 7.0ms (6.3% of total)

ival-neg: 3.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series25.0ms (0.3%)

Memory

-10.6MiB live, 26.9MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 x) x) (patch (/.f64 (sqrt.f64 x) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* -1 (* x (+ (* 1/2 (sqrt (/ 1 x))) (/ 1 x))))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (+ (* -1 (* x (- (+ (* -1 (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 3)))))) (* -3/8 (sqrt (/ 1 x)))) (* 1/2 (/ 1 x))))) (* -1 (+ (* 1/2 (sqrt (/ 1 x))) (/ 1 x)))))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (+ (* -1 (+ (* 1/2 (sqrt (/ 1 x))) (/ 1 x))) (* x (+ (* -1 (* x (+ (* -1 (+ (* -1 (* (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 3))))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* 5/16 (sqrt (/ 1 x))) (+ (* 3/8 (/ 1 x)) (* 1/2 (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 3))))))))))) (* -1 (- (+ (* -1 (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 3)))))) (* -3/8 (sqrt (/ 1 x)))) (* 1/2 (/ 1 x))))))))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 x) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* -3/8 x))) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* x (- (* 5/16 x) 3/8)))) 1) (taylor 0 x) (#s(alt (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt x)) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 x) (* -1 (sqrt x))) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* x (- (* -1/2 (sqrt x)) 1))) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* x (- (* x (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (sqrt x)))) 1))) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (patch #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 x) x) (patch (/.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 x) x) (patch (/.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 x) x) (patch (/.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 x) x) (patch (/.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x))) (patch (/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 x) 1) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* -3/8 x))) 1) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* x (+ 1/2 (* x (- (* 5/16 x) 3/8)))) 1) (taylor 0 x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* -1/2 (sqrt x)) 1))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt x)) (* x (+ 1/2 (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))) 1))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt x)) (* x (+ 1/2 (+ (* 3/8 (sqrt x)) (+ (* 1/2 (sqrt (/ 1 x))) (* x (- (+ (* -5/16 (sqrt x)) (* -1/4 (sqrt (/ 1 x)))) 3/8))))))) 1))) x) (taylor 0 x) (#s(alt (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 (sqrt x)) 1))) x) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) 1))) x) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (/ (+ 1 x) x) (taylor 0 x) (#s(alt (/.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/4 (sqrt x))) x)) (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (* (sqrt x) (pow (sqrt -1) 2))))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (patch (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) (pow x 2))) (* 2 (/ (pow (sqrt -1) 2) x)))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (+ (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 2)))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow x 2))))))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(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)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (patch (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

-inf

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

3.0ms

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

2.0ms

inf

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

simplify155.0ms (1.8%)

Memory

-9.9MiB live, 142.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	679	4438
1	2066	3450
2	7666	3450
0	8022	3241

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 248

Calls

Call 1

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

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

rewrite218.0ms (2.6%)

Memory

-4.5MiB live, 271.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	218
0	70	216
1	265	199
2	2160	197
0	9266	189

Stop Event

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

Counts

21 → 879

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x))
#s(approx (- (+ x 1) x) #s(literal 1 binary64))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64))
(sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x))
(/.f64 (+.f64 x #s(literal 1 binary64)) x)
(-.f64 (+.f64 x #s(literal 1 binary64)) x)
(*.f64 (+.f64 x #s(literal 1 binary64)) x)
(+.f64 x #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
#s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))

Outputs
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eval311.0ms (3.6%)

Memory: 37.7MiB live, 371.8MiB allocated
Compiler: Compiled 49 093 to 5 638 computations (88.5% saved)

prune61.0ms (0.7%)

Memory

22.6MiB live, 143.5MiB allocated

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1 969	8	1 977
Fresh	5	11	16
Picked	4	1	5
Done	2	1	3
Total	1 980	21	2 001

Accuracy

100.0%

Counts

2 001 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 x)))
	40.4%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
	99.6%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
	96.4%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
	40.5%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)))
✓	37.8%	(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	37.8%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	35.9%	(/.f64 (-.f64 #s(approx (sqrt (/ (+ x 1) x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	37.9%	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
	97.9%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
	95.6%	(/.f64 (.f64 #s(literal -1 binary64) #s(approx (- (+ x 1) x) #s(literal 1 binary64))) (.f64 #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.9%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	96.4%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	96.2%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
	7.9%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) #s(literal -1 binary64)) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
✓	32.4%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	80.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x #s(literal -2 binary64)) x)))
	80.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
	96.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)))
	34.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))

Compiler

Compiled 1 177 to 438 computations (62.8% saved)

regimes53.0ms (0.6%)

Memory

-29.6MiB live, 68.2MiB allocated

Counts

55 → 1

Calls

Call 1

Inputs
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) #s(literal -1 binary64)) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(/.f64 (.f64 #s(literal -1 binary64) #s(approx (- (+ x 1) x) #s(literal 1 binary64))) (.f64 #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(approx (sqrt (/ (+ x 1) x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x #s(literal -2 binary64)) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 #s(approx (+ (* (sqrt (+ x 1)) (sqrt x)) x) (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) x)) x))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(/.f64 (*.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (*.f64 (fma.f64 (/.f64 #s(literal 5/4 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) x)))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
(/.f64 (/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (sqrt.f64 x)))
(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) x) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (-.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
(/.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 x x)))
(*.f64 (+.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (-.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(fma.f64 (/.f64 (pow.f64 x #s(literal -3/2 binary64)) (-.f64 (pow.f64 x #s(literal -2 binary64)) (pow.f64 (-.f64 (exp.f64 (neg.f64 (log1p.f64 x))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))) (neg.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -3/2 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (exp.f64 (neg.f64 (log1p.f64 x)))))))

Outputs

(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))

Calls

2 calls:

36.0ms	x
14.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes20.0ms (0.2%)

Memory

-6.3MiB live, 31.3MiB allocated

Counts

33 → 1

Calls

Call 1

Inputs
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) #s(literal -1 binary64)) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(/.f64 (.f64 #s(literal -1 binary64) #s(approx (- (+ x 1) x) #s(literal 1 binary64))) (.f64 #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(approx (sqrt (/ (+ x 1) x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x #s(literal -2 binary64)) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (.f64 (neg.f64 #s(approx (+ (* (sqrt (+ x 1)) (sqrt x)) x) (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) x)) x))
(/.f64 (-.f64 (sqrt.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) x)) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(/.f64 (/.f64 (-.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)) x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) x) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))

Outputs
(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Calls

2 calls:

11.0ms	x
7.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes18.0ms (0.2%)

Memory

-8.8MiB live, 28.1MiB allocated

Counts

28 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

9.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
8.0ms	x

Results

Accuracy	Segments	Branch
99.7%	2	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
99.7%	2	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes13.0ms (0.2%)

Memory

24.6MiB live, 24.6MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

7.0ms	x
5.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.1%)

Memory

-20.9MiB live, 16.4MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms	x

Results

Accuracy	Segments	Branch
96.4%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
96.4%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

3.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
80.7%	1	`x`
80.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
34.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
34.3%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Accuracy

Total -1.4b remaining (-2.3%)

Threshold costs -1.4b (-2.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
7.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
7.9%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch17.0ms (0.2%)

Memory

-22.9MiB live, 18.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
16.0ms	2478212236349577.5	1227454935827148300.0

Samples

7.0ms

64×

valid

Compiler

Compiled 130 to 100 computations (23.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (36.8% of total)

ival-sqrt: 2.0ms (36.8% of total)

adjust: 1.0ms (18.4% of total)

ival-sub: 1.0ms (18.4% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify28.0ms (0.3%)

Memory

13.3MiB live, 50.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	245
1	118	245
2	142	245
3	163	245
4	175	245
5	182	245
6	184	245

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 10000000000000000 binary64)) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))) (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) #s(literal -1 binary64)) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))

Outputs
(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(/.f64 (/.f64 (neg.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)) (neg.f64 x)))
(/.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 #s(approx (* -1 (- (+ x 1) x)) #s(literal -1 binary64))) (*.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 x #s(literal 10000000000000000 binary64)) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))) (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))))
(if (<=.f64 x #s(literal 10000000000000000 binary64)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))) (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x))))
(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (- (+ x 1) x) #s(literal 1 binary64))) #s(approx (+ ( (sqrt (+ 1 x)) (neg (sqrt x))) (neg x)) (fma.f64 #s(literal -2 binary64) x #s(literal -1/2 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt (+ x 1)))) #s(literal -1 binary64)) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt x))) (*.f64 #s(literal -2 binary64) x)))

soundness1.6s (18.5%)

Memory

31.6MiB live, 1 047.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	926	455
3	3322	445
0	8129	416
0	681	4600
1	2082	3717
2	7599	3710
0	8368	3470
0	43	274
0	73	253
1	302	217
2	2644	217
0	8392	217
0	41	218
0	70	216
1	265	199
2	2160	197
0	9266	189
0	510	4444
1	1500	3714
2	4760	3650
0	8871	3437
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	37	223
0	63	221
1	241	196
2	1900	196
0	8748	183
0	679	4438
1	2066	3450
2	7666	3450
0	8022	3241

Stop Event

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

Compiler

Compiled 498 to 299 computations (40% saved)

preprocess113.0ms (1.3%)

Memory: -34.2MiB live, 96.7MiB allocated
Compiler: Compiled 274 to 136 computations (50.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	10	27
1	20	25
2	47	24
3	89	24
4	144	24
5	209	24
6	245	24
7	272	24
8	281	24
0	8	11
0	14	11
1	19	11
2	27	11
3	36	11
4	48	11
5	68	11
6	107	11
7	139	11
8	195	11
9	224	11
10	245	11
11	247	11
0	247	11

Iter	Nodes	Cost
0	8	32
0	14	32
1	19	32
2	27	32
3	36	32
4	48	32
5	68	32
6	107	32
7	139	32
8	195	32
9	224	32
10	245	32
11	247	32
0	247	32

Iter	Nodes	Cost
0	10	27
1	20	25
2	47	24
3	89	24
4	144	24
5	209	24
6	245	24
7	272	24
8	281	24
0	8	11
0	14	11
1	19	11
2	27	11
3	36	11
4	48	11
5	68	11
6	107	11
7	139	11
8	195	11
9	224	11
10	245	11
11	247	11
0	247	11

Iter	Nodes	Cost
0	8	32
0	14	32
1	19	32
2	27	32
3	36	32
4	48	32
5	68	32
6	107	32
7	139	32
8	195	32
9	224	32
10	245	32
11	247	32
0	247	32

start0.0ms (0%)

analyze2.0ms (0%)

sample2.1s (24.1%)

explain182.0ms (2.1%)

preprocess21.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize51.0ms (0.6%)

series6.0ms (0.1%)

simplify203.0ms (2.4%)

rewrite147.0ms (1.7%)

eval85.0ms (1%)

prune30.0ms (0.4%)

simplify118.0ms (1.4%)

localize191.0ms (2.2%)

series134.0ms (1.6%)

simplify273.0ms (3.2%)

rewrite195.0ms (2.3%)

eval623.0ms (7.3%)

prune226.0ms (2.6%)

simplify116.0ms (1.4%)

localize181.0ms (2.1%)

series23.0ms (0.3%)

simplify175.0ms (2.1%)

rewrite194.0ms (2.3%)

eval249.0ms (2.9%)

prune58.0ms (0.7%)

simplify143.0ms (1.7%)

localize198.0ms (2.3%)

series25.0ms (0.3%)

simplify155.0ms (1.8%)

rewrite218.0ms (2.6%)

eval311.0ms (3.6%)

prune61.0ms (0.7%)

regimes53.0ms (0.6%)

regimes20.0ms (0.2%)

regimes18.0ms (0.2%)

regimes13.0ms (0.2%)

regimes12.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

bsearch17.0ms (0.2%)

simplify28.0ms (0.3%)

soundness1.6s (18.5%)

preprocess113.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	27
1	20	25
2	47	24
3	89	24
4	144	24
5	209	24
6	245	24
7	272	24
8	281	24
0	8	11
0	14	11
1	19	11
2	27	11
3	36	11
4	48	11
5	68	11
6	107	11
7	139	11
8	195	11
9	224	11
10	245	11
11	247	11
0	247	11

Iter	Nodes	Cost
0	8	32
0	14	32
1	19	32
2	27	32
3	36	32
4	48	32
5	68	32
6	107	32
7	139	32
8	195	32
9	224	32
10	245	32
11	247	32
0	247	32