Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

4.9MiB live, 4.9MiB 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 (25.3%)

Memory

31.4MiB live, 1 809.4MiB allocated

Samples

1.4s	6 875×	1	valid
284.0ms	1 115×	2	valid
30.0ms	266×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-sqrt: 353.0ms (26.5% of total)

ival-div: 267.0ms (20.1% of total)

adjust: 220.0ms (16.5% of total)

ival-sub: 177.0ms (13.3% of total)

const: 158.0ms (11.9% of total)

ival-add: 81.0ms (6.1% of total)

ival->: 31.0ms (2.3% of total)

ival-<: 20.0ms (1.5% of total)

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

exact: 8.0ms (0.6% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain154.0ms (1.8%)

Memory

-41.5MiB live, 221.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
173	-	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
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	173	0

Confusion

	Predicted +	Predicted -
+	173	1
-	0	82

Precision

1.0

Recall

0.9942528735632183

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	173	0	1
-	0	0	82

Precision?

1.0

Recall?

0.9942528735632183

Freqs

test

number	freq
0	83
1	173

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

60.0ms	436×	1	valid
16.0ms	60×	2	valid
1.0ms	16×	0	valid

Compiler

Compiled 79 to 28 computations (64.6% saved)

Precisions

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

ival-sqrt: 16.0ms (31.4% of total)

ival-div: 14.0ms (27.4% of total)

adjust: 9.0ms (17.6% of total)

ival-add: 6.0ms (11.8% of total)

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

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

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

exact: 0.0ms (0% of total)

preprocess24.0ms (0.3%)

Memory

6.2MiB live, 44.1MiB 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.5%	(-.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)

simplify9.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB 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))

localize56.0ms (0.7%)

Memory

-5.5MiB live, 111.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	38.72271053754724	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

39.0ms	218×	1	valid
8.0ms	30×	2	valid
1.0ms	8×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-div: 12.0ms (36% of total)

ival-sqrt: 8.0ms (24% of total)

adjust: 6.0ms (18% of total)

ival-add: 4.0ms (12% of total)

ival-sub: 2.0ms (6% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

-13.0MiB live, 26.1MiB allocated

Counts

5 → 60

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>) () ())
#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (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 (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>) () ())) ())
#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 x) (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 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (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 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (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 (* 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)))))))) (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 (- (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>) () ())) ())
#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>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
2.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (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))) (sqrt (+ x 1)))

Time

Variable

Point

Expression

5.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify203.0ms (2.4%)

Memory

24.3MiB live, 264.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	155	744
1	437	667
2	1370	639
3	4606	634
0	8302	583

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 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 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))))))))
(- (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))))
(* -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)))))))

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

rewrite131.0ms (1.6%)

Memory

-4.7MiB live, 199.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
0	14	27
1	66	23
2	565	23
3	6719	23
0	8113	23

Stop Event

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

Counts

5 → 285

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

Outputs
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eval101.0ms (1.2%)

Memory: -19.3MiB live, 102.4MiB allocated
Compiler: Compiled 7 270 to 957 computations (86.8% saved)

prune18.0ms (0.2%)

Memory

14.4MiB live, 52.7MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	331	14	345
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	332	14	346

Accuracy

85.0%

Counts

346 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.6%	(/.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))
	40.7%	(/.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)))))
	40.7%	(/.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))))
▶	40.7%	(/.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))))))
	39.6%	(/.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 x)))
	39.6%	(/.f64 (*.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	5.5%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
▶	36.9%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x))))
	27.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	29.9%	(-.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)))))
▶	83.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (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 3 binary64)))) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
	82.9%	#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))))
	66.8%	#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)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 434 to 290 computations (33.2% saved)

simplify149.0ms (1.8%)

Memory

10.9MiB live, 169.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	326
0	74	328
1	119	322
2	248	304
3	699	300
4	2577	299
5	7256	299
0	8383	298

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

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

localize209.0ms (2.5%)

Memory

7.7MiB live, 323.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1875	(/.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))))))
accuracy	0.234375	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
accuracy	0.4453125	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	59.57677049108313	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.234375	(/.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))
accuracy	0.33203125	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	59.80817911960563	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0.234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))
accuracy	1.2283785996695267	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy	38.72271053754724	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.47928434947274	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.7363829386933636	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (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 3 binary64)))) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
accuracy	9.72408252278589	(/.f64 (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 3 binary64)))) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
accuracy	19.9300237964792	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))

Samples

149.0ms	218×	1	valid
23.0ms	30×	2	valid
2.0ms	8×	0	valid

Compiler

Compiled 297 to 39 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 132.0ms

ival-div: 43.0ms (32.6% of total)

ival-mult: 23.0ms (17.4% of total)

adjust: 20.0ms (15.2% of total)

ival-pow: 13.0ms (9.9% of total)

ival-sqrt: 12.0ms (9.1% of total)

ival-add: 11.0ms (8.3% of total)

ival-sub: 7.0ms (5.3% of total)

ival-neg: 2.0ms (1.5% of total)

exact: 1.0ms (0.8% of total)

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

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

series43.0ms (0.5%)

Memory

-27.2MiB live, 48.8MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt x))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (sqrt (/ 1 (pow x 3))) (sqrt (+ x 1)) (/ -1 (sqrt x)))
5.0ms	x	@	0	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt x))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (sqrt (/ 1 (pow x 3))) (sqrt (+ x 1)) (/ -1 (sqrt x)))
4.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/ (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (- (+ x 1) x) (* (- (+ x 1) x) (/ -1 (sqrt x))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (sqrt (/ 1 (pow x 3))) (sqrt (+ x 1)) (/ -1 (sqrt x)))

Time

Variable

Point

Expression

8.0ms

-inf

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

5.0ms

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

4.0ms

inf

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

simplify189.0ms (2.3%)

Memory

25.3MiB live, 222.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	536	4272
1	1652	3565
2	5513	3509
0	8283	3288

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

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

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 7))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 4))
(/.f64 (fma.f64 (.f64 #s(literal -3/8 binary64) (sqrt.f64 x)) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 4 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 x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (.f64 #s(literal -3/8 binary64) (sqrt.f64 x)) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) x)
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (sqrt.f64 x))) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (*.f64 x x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))
(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x)) (*.f64 x x))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) x (sqrt.f64 x)) (*.f64 x x))
(/ (+ (sqrt x) (* x (+ (sqrt (pow x 3)) (* 1/4 (sqrt x))))) (pow x 2))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) x (sqrt.f64 x)) (*.f64 x 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))
(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 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (+ 1/2 (* -1/2 (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (* 3/8 (- 1 (sqrt x))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64) #s(literal -3/8 binary64)) x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (+ (* -1/2 (- 1 (sqrt x))) (* x (- (+ (* 3/8 (- 1 (sqrt x))) (* x (+ 5/16 (* -5/16 (- 1 (sqrt x)))))) 3/8)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -5/16 binary64) #s(literal 5/16 binary64)) x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64) #s(literal -3/8 binary64))) x (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 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 (-.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 #s(literal -1/8 binary64) (sqrt.f64 x) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 #s(literal -1/8 binary64) (sqrt.f64 x) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (+ 1 (sqrt x)))
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x))))
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(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (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)
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(* -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 (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))
(* 2 (* x (pow (sqrt -1) 2)))
(*.f64 #s(literal -2 binary64) x)
(* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 x x) #s(literal -3/2 binary64))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 (.f64 #s(literal -1/8 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x) #s(literal -3/2 binary64))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal -2 binary64) x) (/.f64 #s(literal 3/2 binary64) (.f64 x x))) (/.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 -1/8 binary64) x) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(* -1 (sqrt (/ 1 x)))
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(* -1 (sqrt (/ 1 x)))
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(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
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(* 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))
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(/ (+ (* -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))
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(/ (+ (* -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))
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(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
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(* -1 (* (sqrt 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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
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(* -1 (sqrt (/ 1 x)))
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(* -1 (sqrt (/ 1 x)))
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rewrite175.0ms (2.1%)

Memory

-12.7MiB live, 177.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	255
0	74	236
1	299	200
2	2541	200
0	9056	200

Stop Event

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

Counts

22 → 1 002

Calls

Call 1

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

Outputs
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eval283.0ms (3.4%)

Memory: 9.3MiB live, 285.4MiB allocated
Compiler: Compiled 40 477 to 4 636 computations (88.5% saved)

prune52.0ms (0.6%)

Memory

-10.0MiB live, 117.6MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1 630	18	1 648
Fresh	8	1	9
Picked	4	1	5
Done	0	0	0
Total	1 642	20	1 662

Accuracy

100.0%

Counts

1 662 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.1%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.5%	(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.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)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
	97.6%	(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
	40.7%	(/.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))))
	39.6%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
▶	39.6%	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
	40.7%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
	39.7%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 x x) #s(literal -3/2 binary64))))
	98.4%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
	97.7%	(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
▶	99.3%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (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 (+.f64 x #s(literal 1 binary64))))))
	39.6%	(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
	83.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (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 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) x))
	82.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x)))
	82.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	82.9%	#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))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	97.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))

Compiler

Compiled 641 to 437 computations (31.8% saved)

simplify182.0ms (2.2%)

Memory

12.5MiB live, 234.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
cost-diff	0	#s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
cost-diff	1536	(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
cost-diff	0	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff	128	(*.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	192	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(/.f64 x (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
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	(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	#s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (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 (+.f64 x #s(literal 1 binary64))))))
cost-diff	896	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	369
0	87	369
1	139	365
2	262	337
3	540	335
4	1235	333
5	4450	333
0	8262	320

Stop Event

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

Calls

Call 1

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

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

localize383.0ms (4.6%)

Memory

0.7MiB live, 413.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1796875	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x)
accuracy	0.1953125	(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
accuracy	0.7363829386933636	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
accuracy	1.2983080290888278	#s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
accuracy	0.01171875	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) (+.f64 x #s(literal 1 binary64)))
accuracy	0.234375	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	29.55127048404636	(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x))
accuracy	59.96335142618389	(-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.00390625	(sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))
accuracy	0.234375	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
accuracy	58.823167757443954	(-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))
accuracy	0	(sqrt.f64 x)
accuracy	0.234375	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.47928434947274	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.1875	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (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 (+.f64 x #s(literal 1 binary64))))))
accuracy	0.4453125	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

147.0ms	146×	1	valid
145.0ms	102×	2	valid
2.0ms	8×	0	valid

Compiler

Compiled 293 to 52 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-div: 96.0ms (40.5% of total)

adjust: 58.0ms (24.5% of total)

ival-mult: 25.0ms (10.5% of total)

ival-sqrt: 22.0ms (9.3% of total)

ival-add: 14.0ms (5.9% of total)

ival-sub: 10.0ms (4.2% of total)

ival-neg: 8.0ms (3.4% of total)

ival-pow: 3.0ms (1.3% of total)

exact: 1.0ms (0.4% of total)

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

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

series123.0ms (1.5%)

Memory

-9.7MiB live, 28.2MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

-inf

((* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg (sqrt (/ 1 x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ (- 1 (sqrt (/ x (+ x 1)))) (sqrt x)) (- 1 (sqrt (/ x (+ x 1)))) (sqrt (/ x (+ x 1))) (/ x (+ x 1)) (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (* (+ x 1) x) (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) (- (+ x 1) (sqrt (* (+ x 1) x))) (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/ (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) x) (sqrt (/ 1 x)) (sqrt (+ x 1)) (sqrt (* (+ x 1) x)) (/ (sqrt (/ 1 x)) x))

5.0ms

((* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg (sqrt (/ 1 x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ (- 1 (sqrt (/ x (+ x 1)))) (sqrt x)) (- 1 (sqrt (/ x (+ x 1)))) (sqrt (/ x (+ x 1))) (/ x (+ x 1)) (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (* (+ x 1) x) (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) (- (+ x 1) (sqrt (* (+ x 1) x))) (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/ (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) x) (sqrt (/ 1 x)) (sqrt (+ x 1)) (sqrt (* (+ x 1) x)) (/ (sqrt (/ 1 x)) x))

3.0ms

inf

((* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1))))) (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg (sqrt (/ 1 x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ (- 1 (sqrt (/ x (+ x 1)))) (sqrt x)) (- 1 (sqrt (/ x (+ x 1)))) (sqrt (/ x (+ x 1))) (/ x (+ x 1)) (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (* (+ x 1) x) (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) (- (+ x 1) (sqrt (* (+ x 1) x))) (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/ (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) x) (sqrt (/ 1 x)) (sqrt (+ x 1)) (sqrt (* (+ x 1) x)) (/ (sqrt (/ 1 x)) x))

simplify270.0ms (3.2%)

Memory

-2.7MiB live, 118.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	698	4355
1	2162	3544
2	7227	3526
0	8098	3360

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 273

Calls

Call 1

Inputs
(* -1 (+ 1 (sqrt x)))
(+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (* x (+ 1/8 (* -1/8 (+ 1 (sqrt x)))))) (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))) (* x (+ (* -1 (* x (- (* 1/16 (+ 1 (sqrt x))) 1/16))) (* -1 (+ 1/8 (* -1/8 (+ 1 (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 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 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 x)
(sqrt x)
(sqrt x)
(sqrt x)
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* 1/2 (pow x 2)) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (* (pow x 2) (+ 1/2 (* -1/2 x)))) x)
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (* (pow x 2) (+ 1/2 (* x (- (* 1/2 (* x (+ 1 (* 1/4 (/ 1 x))))) 1/2))))) x)
(- 1 (sqrt x))
(- (+ 1 (* 1/2 (sqrt (pow x 3)))) (sqrt x))
(- (+ 1 (* (pow x 2) (- (* -1/2 (sqrt x)) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x))
(- (+ 1 (* (pow x 2) (- (* x (- (* 1/2 (* (sqrt x) (+ 1 (* 1/4 (/ 1 x))))) (* 1/2 (sqrt (/ 1 x))))) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x))
(sqrt x)
(+ (sqrt x) (* -1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1/2 (* (sqrt x) (+ 1 (* 1/4 (/ 1 x))))) (* 1/2 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* -1 x)))
(* x (+ 1 (* x (- x 1))))
(* x (+ 1 (* x (- (* x (+ 1 (* -1 x))) 1))))
(- 1 (sqrt x))
(- (+ 1 (sqrt (pow x 3))) (sqrt x))
(- (+ 1 (* x (+ (sqrt x) (* x (- (* -1/2 (sqrt (/ 1 x))) (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (- (sqrt x) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x)))))) (sqrt x))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(* (sqrt (/ 1 x)) (- 1 (sqrt x)))
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (pow x 2)) x)
(/ (+ (* x (+ x (* (sqrt (pow x 3)) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/ (+ (* x (+ x (* x (+ (* (sqrt x) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))) (* (sqrt (pow x 3)) (- (sqrt x) (* -1/2 (sqrt (/ 1 x))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(- 1 (sqrt x))
(- (+ 1 x) (sqrt x))
(- (+ 1 (* x (+ 1 (* -1/2 (sqrt x))))) (sqrt x))
(- (+ 1 (* x (+ 1 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (sqrt x))
(* 5/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(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 7))))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))) (pow x 4))
(* 5/8 (sqrt (/ 1 (pow x 5))))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(+ (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 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* -2 x)
(* -1 (* (pow x 2) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (pow x 2))))))
(* (pow x 2) (- (/ 1/8 (pow x 3)) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (pow x 2))))))
(* (pow x 2) (- (+ (* -1 (/ (- (* 3/16 (pow x 2)) (* 1/8 (pow x 2))) (pow x 6))) (* 1/8 (/ 1 (pow x 3)))) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (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))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 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 x)
(sqrt x)
(sqrt x)
(sqrt x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* -35/128 (sqrt (/ 1 (pow x 7)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ 1/2 x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 35/128 (/ 1 (pow x 3))))) x)
1
(- 1 (* 1/2 (/ 1 x)))
(- (+ 1 (/ 3/8 (pow x 2))) (* 1/2 (/ 1 x)))
(- (+ 1 (/ 3/8 (pow x 2))) (+ (* 1/2 (/ 1 x)) (* 5/16 (/ 1 (pow x 3)))))
1
(- 1 (/ 1 x))
(- (+ 1 (/ 1 (pow x 2))) (/ 1 x))
(- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3))))
(/ 1/2 x)
(/ (- 1/2 (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 3/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 3/8 (/ 1 x)) (* 35/128 (/ 1 (pow x 3))))) 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))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* -35/128 (sqrt (/ 1 (pow x 7)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(- (+ 1/2 (* 1/8 (/ 1 x))) (/ 1/16 (pow x 2)))
(- (+ 1/2 (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) (/ 1/16 (pow x 2)))
(* 1/2 (sqrt (/ 1 x)))
(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 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)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5))))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 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))))))))
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))))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* 2 (* x (pow (sqrt -1) 2)))
(* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (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))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -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)))
(- (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)) (- 1 (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (- 1 (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (- 1 (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))))) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2))))))) x)) (* 1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (- 1 (pow (sqrt -1) 2))))
(- 1 (pow (sqrt -1) 2))
(- 1 (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ 1 (* -1 (/ (+ 1/2 (* -1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) x))) x))) (pow (sqrt -1) 2))
(- (+ 1 (* -1 (/ (+ 1/2 (* -1 (/ (- (* -1/2 (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) x)) (* -1/2 (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))))) x))) x))) (pow (sqrt -1) 2))
(pow (sqrt -1) 2)
(+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1 (/ (- (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (pow (sqrt -1) 2))
(+ (* -1 (/ (- (* -1 (/ (+ (* -1/2 (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2))))) (* 1/2 (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) x))) x)) 1/2) x)) (pow (sqrt -1) 2))
1
(- 1 (/ 1 x))
(+ 1 (* -1 (/ (- 1 (/ 1 x)) x)))
(+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 x)) x))) x)))
(+ 1 (pow (sqrt -1) 2))
(+ 1 (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) x)) (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(+ 1 (+ (* -1 (/ (- (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) x)) (+ (/ 1/8 (* x (pow (sqrt -1) 2))) (* 1/2 (/ 1 x)))) (+ 1/2 (* -1 (+ 1 (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)))
(+ 1 (+ (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 (pow (sqrt -1) 4))) (+ 1/2 (+ (* -1 (+ 1 (pow (sqrt -1) 2))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))))) x)) (+ 1/2 (+ (* -1 (+ 1 (pow (sqrt -1) 2))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))))) x)) (+ 1/2 (* -1 (+ 1 (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (sqrt (/ 1 x)) (+ 1 (pow (sqrt -1) 2)))
(+ (* (sqrt (/ 1 x)) (+ 1 (pow (sqrt -1) 2))) (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (* 1/2 (/ 1 (sqrt -1)))))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (* 1/2 (/ 1 (sqrt -1))))))) (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (+ (* 1/8 (/ 1 (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) x)) (* (sqrt (/ 1 x)) (+ 1 (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (* 1/2 (/ 1 (sqrt -1))))))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (+ (* 1/8 (/ 1 (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- (* 1/16 (/ 1 (pow (sqrt -1) 5))) (+ (* -1 (/ (+ 1 (pow (sqrt -1) 2)) (sqrt -1))) (+ (* 1/8 (/ 1 (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))))) x))) x)) (* (sqrt (/ 1 x)) (+ 1 (pow (sqrt -1) 2))))
(* x (+ 1 (pow (sqrt -1) 2)))
(* x (+ 1 (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x))) x)) (+ 1 (pow (sqrt -1) 2)))))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (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))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -1 (* (sqrt x) (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))))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))

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

rewrite336.0ms (4%)

Memory

23.9MiB live, 136.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	314
0	87	307
1	347	265
2	2904	265
0	9130	250

Stop Event

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

Counts

23 → 656

Calls

Call 1

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

Outputs
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eval234.0ms (2.8%)

Memory: 3.1MiB live, 240.6MiB allocated
Compiler: Compiled 22 747 to 3 980 computations (82.5% saved)

prune95.0ms (1.1%)

Memory

-2.9MiB live, 121.9MiB allocated

Pruning

28 alts after pruning (25 fresh and 3 done)

	Pruned	Kept	Total
New	1 127	16	1 143
Fresh	5	9	14
Picked	3	2	5
Done	0	1	1
Total	1 135	28	1 163

Accuracy

100.0%

Counts

1 163 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.1%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.6%	(/.f64 (/.f64 #s(approx (- (+ x 1) (sqrt (* (+ x 1) x))) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.8%	(/.f64 (/.f64 #s(approx (- (+ x 1) (sqrt (* (+ x 1) x))) #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.5%	(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.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)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
	40.7%	(/.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))))
	39.6%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
✓	39.6%	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
	38.3%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (/ x (+ x 1))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 x))
	39.7%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 x x) #s(literal -3/2 binary64))))
	99.2%	(/.f64 (neg.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	98.9%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
▶	98.4%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
	97.7%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
▶	36.9%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
▶	99.3%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
	97.4%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (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 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))))
	83.8%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (.f64 (-.f64 (/.f64 #s(literal -3/2 binary64) (.f64 x x)) (/.f64 #s(literal 2 binary64) x)) (*.f64 x x))))
	98.2%	(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))
	39.6%	(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) x))
▶	82.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x)))
	82.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	82.9%	#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))))
✓	5.5%	#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 (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) x)))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
	96.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 5/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))

Compiler

Compiled 807 to 584 computations (27.6% saved)

simplify147.0ms (1.8%)

Memory

4.0MiB live, 234.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x)))
cost-diff	832	(.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
cost-diff	1536	(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
cost-diff	0	(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)
cost-diff	0	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
cost-diff	0	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))
cost-diff	0	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
cost-diff	0	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x))
cost-diff	0	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64))
cost-diff	0	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
cost-diff	0	(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	#s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
cost-diff	2048	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	517
0	98	507
1	160	493
2	289	459
3	634	459
4	1506	451
5	5338	451
0	8165	430

Stop Event

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

Calls

Call 1

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

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

localize307.0ms (3.7%)

Memory

7.4MiB live, 409.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.28515625	(.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
accuracy	0.7363829386933636	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x)))
accuracy	1.3061112934676047	#s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
accuracy	9.72408252278589	(/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (*.f64 x x))
accuracy	0.01171875	(-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x))
accuracy	0.234375	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
accuracy	0.45874181598722	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 5/16 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 3/8 binary64) x)) x))
accuracy	0.875561541949804	(/.f64 #s(literal 5/16 binary64) (*.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.0078125	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
accuracy	0.234375	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
accuracy	0.7483842256252583	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.234375	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
accuracy	60.53456243966887	#s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64))
accuracy	0.09765625	(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.1875	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
accuracy	0.44140625	(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Samples

217.0ms	218×	1	valid
28.0ms	30×	2	valid
3.0ms	8×	0	valid

Compiler

Compiled 383 to 61 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

adjust: 77.0ms (37.6% of total)

ival-div: 42.0ms (20.5% of total)

ival-mult: 28.0ms (13.7% of total)

ival-add: 18.0ms (8.8% of total)

ival-sqrt: 18.0ms (8.8% of total)

ival-sub: 13.0ms (6.4% of total)

ival-pow: 3.0ms (1.5% of total)

ival-neg: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series34.0ms (0.4%)

Memory

-0.4MiB live, 36.1MiB allocated

Counts

23 → 276

Calls

Call 1

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

Outputs
#s(alt (- (* -1 (sqrt x)) 1) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 x) (* -1 (sqrt x))) 1) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (sqrt x)) (* x (- (* -1/2 (sqrt x)) 1))) 1) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (sqrt x)) (* x (- (* x (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (sqrt x)))) 1))) 1) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (patch (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

14.0ms

-inf

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

4.0ms

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

3.0ms

inf

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

simplify143.0ms (1.7%)

Memory

2.7MiB live, 158.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	504	4810
1	1507	3821
2	5335	3441
0	8244	3266

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

Outputs
(- (* -1 (sqrt x)) 1)
(-.f64 #s(literal -1 binary64) (sqrt.f64 x))
(- (+ (* -1 x) (* -1 (sqrt x))) 1)
(-.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) x)
(- (+ (* -1 (sqrt x)) (* x (- (* -1/2 (sqrt x)) 1))) 1)
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) #s(literal -1 binary64)) x (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(- (+ (* -1 (sqrt x)) (* x (- (* x (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (sqrt x)))) 1))) 1)
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x #s(literal -1 binary64)) x (-.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(* -1 (* (sqrt (/ 1 x)) (/ 1 (- (* -1 (sqrt x)) 1))))
(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))) x)
(/.f64 (-.f64 (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* x (+ (* -1 (* (sqrt x) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))) (* -1 (* (sqrt (pow x 3)) (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))))))))) x)
(/.f64 (fma.f64 (neg.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (/.f64 (sqrt.f64 x) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))) x (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* x (+ (* -1 (* (sqrt x) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))) (* x (+ (* -1 (* (sqrt x) (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))))) (* (sqrt (pow x 3)) (+ (* -1 (/ (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))) (- (* -1 (sqrt x)) 1))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 3))))))))))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 x)))) x (/.f64 (neg.f64 (sqrt.f64 x)) (pow.f64 (-.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 2 binary64)))) x (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) x)
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (sqrt (/ 1 x)))
(neg.f64 (sqrt.f64 (/.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)))
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (pow x 2)) x)
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x)) x)
(/ (+ (* x (+ x (* (sqrt (pow x 3)) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ x (* x (+ (* (sqrt x) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))) (* (sqrt (pow x 3)) (- (sqrt x) (* -1/2 (sqrt (/ 1 x))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 x))) x 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 (sqrt (pow x 3))) (sqrt x))
(+.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (* -1/2 (sqrt (/ 1 x))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (- (sqrt x) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 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 (sqrt x)))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (pow x 2)) x)
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x)) x)
(/ (+ (* x (+ x (* (sqrt (pow x 3)) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ x (* x (+ (* (sqrt x) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))) (* (sqrt (pow x 3)) (- (sqrt x) (* -1/2 (sqrt (/ 1 x))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 x))) x 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 (sqrt (pow x 3))) (sqrt x))
(+.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (* -1/2 (sqrt (/ 1 x))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (- (sqrt x) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ -3/8 (pow x 2))
(/.f64 (/.f64 #s(literal -3/8 binary64) x) x)
(/ (- (* 1/2 x) 3/8) (pow x 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
(/ (- (* 1/2 x) 3/8) (pow x 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
(/ (- (* 1/2 x) 3/8) (pow x 2))
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)
(/ -3/8 x)
(/.f64 #s(literal -3/8 binary64) x)
(/ (- (* 1/2 x) 3/8) x)
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))
(/ (- (* 1/2 x) 3/8) x)
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))
(/ (- (* 1/2 x) 3/8) x)
(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 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)))
(/ (+ (* (sqrt x) (- 1 (sqrt x))) (pow x 2)) x)
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x x)) x)
(/ (+ (* x (+ x (* (sqrt (pow x 3)) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) x (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x)
(/ (+ (* x (+ x (* x (+ (* (sqrt x) (- (* -1/2 (sqrt (/ 1 x))) (sqrt x))) (* (sqrt (pow x 3)) (- (sqrt x) (* -1/2 (sqrt (/ 1 x))))))))) (* (sqrt x) (- 1 (sqrt x)))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 x))) x 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 (sqrt (pow x 3))) (sqrt x))
(+.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (* -1/2 (sqrt (/ 1 x))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ (sqrt x) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (- (sqrt x) (* -1/2 (sqrt (/ 1 x)))))) (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))) x (sqrt.f64 x)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ 5/16 (pow x 3))
(/.f64 #s(literal 5/16 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 5/16 (* -3/8 x)) (pow x 3))
(/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 5/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 5/16 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -3/8 binary64)) x #s(literal 5/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 5/16 (* x (- (* 1/2 x) 3/8))) (pow x 3))
(/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -3/8 binary64)) x #s(literal 5/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ 5/16 (pow x 2))
(/.f64 #s(literal 5/16 binary64) (*.f64 x x))
(/ (+ 5/16 (* -3/8 x)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 5/16 binary64)) x) x)
(/ (+ 5/16 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -3/8 binary64)) x #s(literal 5/16 binary64)) x) x)
(/ (+ 5/16 (* x (- (* 1/2 x) 3/8))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -3/8 binary64)) x #s(literal 5/16 binary64)) x) x)
(* 5/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 5/8 binary64))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* 5/8 (sqrt (/ 1 x)))
(*.f64 #s(literal 5/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 5/8 binary64) (sqrt.f64 x))) 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)
(* 1/2 (sqrt (/ 1 (pow x 7))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/2 binary64))
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1/2
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(+ 1/2 (* -1 (/ (- 3/8 (* 5/16 (/ 1 x))) x)))
(+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64))
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(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
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(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
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(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
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(* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(* -1 (* x (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(* -1 (* x (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(- (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))))
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(+.f64 (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.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))))
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(* -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 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
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(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
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(/ 5/16 (pow x 2))
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(/ 5/16 (pow x 2))
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(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
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rewrite183.0ms (2.2%)

Memory

-3.3MiB live, 195.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	443
0	98	424
1	424	368
2	3733	360
0	9346	333

Stop Event

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

Counts

23 → 528

Calls

Call 1

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

Outputs
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eval121.0ms (1.4%)

Memory: 33.3MiB live, 187.0MiB allocated
Compiler: Compiled 21 748 to 3 241 computations (85.1% saved)

prune330.0ms (3.9%)

Memory

-191.5MiB live, 117.0MiB allocated

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	979	10	989
Fresh	6	14	20
Picked	4	1	5
Done	0	3	3
Total	989	28	1 017

Accuracy

100.0%

Counts

1 017 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.1%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x x))) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.8%	(/.f64 (/.f64 #s(approx (- (+ x 1) (sqrt (* (+ x 1) x))) #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	98.5%	(/.f64 (/.f64 #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.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)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
	40.7%	(/.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))))
	39.6%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
✓	39.6%	(/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
	38.3%	(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (/ x (+ x 1))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 x))
	83.6%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 x (/.f64 #s(literal 3/8 binary64) x))) (*.f64 x x))) (sqrt.f64 x))
✓	98.4%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)) (sqrt.f64 x))
	98.9%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
	97.7%	(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(approx (- (+ (/ 5/16 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
	99.6%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
	97.4%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (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 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))))
	99.1%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (+ (* (sqrt (+ 1 x)) (neg (sqrt (+ 1 x)))) (* (sqrt x) (neg (sqrt (+ 1 x))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x (fma.f64 #s(literal -2 binary64) x #s(literal -3/2 binary64)))))
	98.6%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (+ (* (sqrt (+ 1 x)) (neg (sqrt (+ 1 x)))) (* (sqrt x) (neg (sqrt (+ 1 x))))) (fma.f64 #s(literal -2 binary64) x #s(literal -3/2 binary64))))
	97.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x))))
	98.2%	(/.f64 #s(literal 1 binary64) (.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))
	98.4%	(.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(approx (/ (- (+ x 1) (sqrt ( (+ x 1) x))) (+ x 1)) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) x)))
	39.6%	(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 x (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
	36.9%	#s(approx (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) #s(literal 0 binary64))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) x))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(approx (+ ( (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)) (.f64 x x)))
	82.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	82.9%	#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))))
✓	5.5%	#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 (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
	96.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 5/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))

Compiler

Compiled 1 281 to 537 computations (58.1% saved)

regimes33.0ms (0.4%)

Memory

-3.7MiB live, 34.1MiB allocated

Counts

59 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

16.0ms	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)

regimes53.0ms (0.6%)

Memory

-11.2MiB live, 27.0MiB allocated

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

43.0ms	x
8.0ms	(-.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
99.1%	1	`x`
99.1%	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)

regimes22.0ms (0.3%)

Memory

-11.1MiB live, 26.9MiB allocated

Counts

30 → 1

Calls

Call 1

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

Outputs
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 5/16 binary64) x) #s(literal 3/8 binary64)) x) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))

Calls

2 calls:

13.0ms	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
98.9%	1	`x`
98.9%	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)

regimes16.0ms (0.2%)

Memory

26.2MiB live, 26.2MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

8.0ms	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
98.6%	1	`x`
98.6%	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)

regimes9.0ms (0.1%)

Memory

-24.7MiB live, 12.6MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) #s(literal 0 binary64))
#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)))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(approx (- (+ (/ 5/16 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))
(/.f64 (/.f64 #s(approx (- (+ x 1) (sqrt (* (+ x 1) x))) #s(literal 1/2 binary64)) (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* 1/2 (sqrt (/ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
(/.f64 (-.f64 #s(literal 1 binary64) #s(approx (sqrt (/ x (+ x 1))) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 x))

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

Calls

2 calls:

6.0ms	x
3.0ms	(-.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
97.8%	1	`x`
97.8%	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)

regimes6.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) #s(literal 0 binary64))
#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)))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(/.f64 #s(approx (/ (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (/.f64 #s(approx (- (+ (/ 5/16 (* x x)) 1/2) (/ 3/8 x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 x))

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

Calls

2 calls:

3.0ms	x
3.0ms	(-.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
97.7%	1	`x`
97.7%	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

8.5MiB live, 8.5MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) #s(literal 0 binary64))
#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)))
(/.f64 #s(approx (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) #s(literal 0 binary64)) (sqrt.f64 x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 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 (+ (* (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x)) 1/2) (* -1/2 (sqrt (/ 1 x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.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
82.9%	1	`x`
82.9%	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)

regimes4.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total -20.9b remaining (-51.7%)

Threshold costs -20.9b (-51.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (/ (- (+ x 1) (sqrt (* (+ x 1) x))) (+ x 1)) (sqrt x)) #s(literal 0 binary64))

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
36.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
36.9%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

simplify27.0ms (0.3%)

Memory

-23.6MiB live, 51.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	249
1	95	249
2	102	249
3	106	249
4	107	249

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (15.7%)

Memory

28.0MiB live, 931.0MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	504	4810
1	1507	3821
2	5335	3441
0	8244	3266
0	536	4272
1	1652	3565
2	5513	3509
0	8283	3288
0	155	744
1	437	667
2	1370	639
3	4606	634
0	8302	583
0	68	443
0	98	424
1	424	368
2	3733	360
0	9346	333
0	43	255
0	74	236
1	299	200
2	2541	200
0	9056	200
0	8	27
0	14	27
1	66	23
2	565	23
3	6719	23
0	8113	23
0	698	4355
1	2162	3544
2	7227	3526
0	8098	3360
0	59	314
0	87	307
1	347	265
2	2904	265
0	9130	250

Stop Event

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

Compiler

Compiled 544 to 278 computations (48.9% saved)

preprocess74.0ms (0.9%)

Memory: 7.7MiB live, 127.1MiB allocated
Compiler: Compiled 226 to 124 computations (45.1% 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 (25.3%)

explain154.0ms (1.8%)

preprocess24.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.1%)

localize56.0ms (0.7%)

series10.0ms (0.1%)

simplify203.0ms (2.4%)

rewrite131.0ms (1.6%)

eval101.0ms (1.2%)

prune18.0ms (0.2%)

simplify149.0ms (1.8%)

localize209.0ms (2.5%)

series43.0ms (0.5%)

simplify189.0ms (2.3%)

rewrite175.0ms (2.1%)

eval283.0ms (3.4%)

prune52.0ms (0.6%)

simplify182.0ms (2.2%)

localize383.0ms (4.6%)

series123.0ms (1.5%)

simplify270.0ms (3.2%)

rewrite336.0ms (4%)

eval234.0ms (2.8%)

prune95.0ms (1.1%)

simplify147.0ms (1.8%)

localize307.0ms (3.7%)

series34.0ms (0.4%)

simplify143.0ms (1.7%)

rewrite183.0ms (2.2%)

eval121.0ms (1.4%)

prune330.0ms (3.9%)

regimes33.0ms (0.4%)

regimes53.0ms (0.6%)

regimes22.0ms (0.3%)

regimes16.0ms (0.2%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify27.0ms (0.3%)

soundness1.3s (15.7%)

preprocess74.0ms (0.9%)

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