Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

3.1MiB live, 3.1MiB 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)

sample1.9s (21.8%)

Memory

25.2MiB live, 1 752.3MiB allocated

Samples

1.2s	6 816×	1	valid
321.0ms	1 157×	2	valid
21.0ms	283×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 309.0ms (25% of total)

ival-div: 302.0ms (24.4% of total)

adjust: 165.0ms (13.3% of total)

ival-sub: 148.0ms (12% of total)

ival-add: 123.0ms (9.9% of total)

const: 121.0ms (9.8% of total)

ival->: 30.0ms (2.4% of total)

ival-<: 19.0ms (1.5% of total)

ival-and: 11.0ms (0.9% of total)

exact: 7.0ms (0.6% of total)

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

Bogosity

explain162.0ms (1.8%)

Memory

8.3MiB live, 86.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
176	2	(1.827712034451763e+215)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`	cancellation	178	0

Confusion

	Predicted +	Predicted -
+	176	0
-	2	78

Precision

0.9887640449438202

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	176	0	0
-	2	0	78

Precision?

0.9887640449438202

Recall?

1.0

Freqs

test

number	freq
0	78
1	178

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

53.0ms	426×	1	valid
15.0ms	78×	2	valid
0.0ms	8×	0	valid

Compiler

Compiled 80 to 28 computations (65% saved)

Precisions

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

ival-sqrt: 15.0ms (31.4% of total)

ival-div: 13.0ms (27.2% of total)

adjust: 9.0ms (18.8% of total)

ival-add: 5.0ms (10.5% of total)

ival-sub: 4.0ms (8.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess73.0ms (0.8%)

Memory

-28.1MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
52×	`lower-+.f32`

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.7%	(-.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 8 computations (33.3% saved)

simplify11.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB 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)))))

Rules

112×	`lower-fma.f64`
112×	`lower-fma.f32`
80×	`lower-*.f64`
80×	`lower-*.f32`
52×	`lower-+.f32`

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

localize45.0ms (0.5%)

Memory

22.8MiB live, 22.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	39.17128429377308	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

26.0ms	213×	1	valid
7.0ms	39×	2	valid
0.0ms	4×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-div: 7.0ms (30% of total)

ival-sqrt: 7.0ms (30% of total)

adjust: 5.0ms (21.4% of total)

ival-add: 2.0ms (8.6% of total)

ival-sub: 2.0ms (8.6% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

simplify437.0ms (5%)

Memory

-12.0MiB live, 261.2MiB allocated

Algorithm

1×	egg-herbie

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
4 828×	`lower-*.f64`
4 828×	`lower-*.f32`
3 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite210.0ms (2.4%)

Memory

-4.4MiB live, 264.7MiB allocated

Rules

4 400×	`lower-fma.f64`
4 400×	`lower-fma.f32`
3 040×	`lower-*.f64`
3 040×	`lower-*.f32`
2 738×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

4 → 238

Calls

Call 1

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

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

eval33.0ms (0.4%)

Memory: -0.8MiB live, 74.9MiB allocated
Compiler: Compiled 7 402 to 706 computations (90.5% saved)

prune46.0ms (0.5%)

Memory

-17.5MiB live, 104.4MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	277	9	286
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	277	10	287

Accuracy

83.4%

Counts

287 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	40.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	38.8%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
✓	38.7%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	27.7%	(-.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)))))
	40.9%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	83.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
▶	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
	68.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 308 to 182 computations (40.9% saved)

simplify182.0ms (2.1%)

Memory

-7.0MiB live, 309.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
cost-diff	0	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))

Rules

10 680×	`lower-fma.f32`
10 674×	`lower-fma.f64`
2 914×	`lower-*.f32`
2 904×	`lower-*.f64`
1 902×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	362
0	71	342
1	131	338
2	252	338
3	499	338
4	1207	338
5	3057	338
6	6599	338
0	8094	338

Stop Event

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

Calls

Call 1

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

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

localize216.0ms (2.5%)

Memory

13.0MiB live, 488.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
accuracy	1.128009302813104	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
accuracy	30.72320694668863	(sqrt.f64 (fma.f64 x x x))
accuracy	59.57677049108313	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
accuracy	0.8802069479857968	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
accuracy	9.713493376906952	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
accuracy	0	#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.2421875	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	39.17128429377308	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.47227185889832	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.13010041222651253	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	0.183902536933087	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
accuracy	10.723963737883734	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
accuracy	19.720584242970258	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

99.0ms	213×	1	valid
33.0ms	39×	2	valid
1.0ms	4×	0	valid

Compiler

Compiled 321 to 37 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-sqrt: 24.0ms (24.4% of total)

ival-div: 18.0ms (18.3% of total)

adjust: 17.0ms (17.3% of total)

ival-mult: 14.0ms (14.2% of total)

ival-add: 13.0ms (13.2% of total)

ival-sub: 10.0ms (10.2% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.3%)

Memory

13.8MiB live, 52.0MiB allocated

Counts

21 → 252

Calls

Call 1

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

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

Calls

63 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(sqrt (/ 1 (* x (* x x))))
1.0ms	x	@	0	(/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))))
1.0ms	x	@	-inf	(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
1.0ms	x	@	0	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
1.0ms	x	@	-inf	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))

simplify296.0ms (3.4%)

Memory

-23.1MiB live, 381.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 980×	`lower-fma.f64`
11 980×	`lower-fma.f32`
5 848×	`lower-*.f64`
5 848×	`lower-*.f32`
4 156×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	410	3863
1	1223	3267
2	4155	3238
0	8201	3069

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 249

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

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

rewrite302.0ms (3.4%)

Memory

19.1MiB live, 441.8MiB allocated

Rules

7 000×	`lower-fma.f32`
6 994×	`lower-fma.f64`
4 644×	`lower-/.f32`
4 632×	`lower-/.f64`
3 866×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	270
0	71	250
1	307	211
2	2629	206
0	9342	204

Stop Event

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

Counts

21 → 881

Calls

Call 1

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

Outputs
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x (neg.f64 x))) (/.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64)) (.f64 x x)))
(neg.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) x)))
(/.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64)) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x) x)
(/.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64))) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x)) (neg.f64 x))
(/.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x)
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64)))) (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) #s(literal 1 binary64))) (.f64 x (neg.f64 x)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) (neg.f64 x))
(pow.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) x) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x))
(.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal -1/2 binary64) (/.f64 (neg.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (*.f64 x x)))
(.f64 (.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))))
(.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x))
(.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 #s(literal 1/2 binary64) x))
(.f64 (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) x) (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (neg.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) x))
(.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (neg.f64 x)))
(.f64 (/.f64 (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (*.f64 x x)) #s(literal 1/2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))) (neg.f64 x)))
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#s(literal 1 binary64)
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(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (/.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x) (.f64 (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))))
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(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))) x (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
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(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)))
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64)))
(exp.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64) (.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 3 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (.f64 x x))))
(/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x))) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (.f64 x (.f64 x x))))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 x))) (neg.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal 3 binary64)) (neg.f64 (.f64 x (sqrt.f64 x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 (*.f64 x (neg.f64 x))))
(pow.f64 x #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 6 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal -2 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64))
(pow.f64 (neg.f64 (neg.f64 (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (sqrt.f64 x)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) (.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 x (fma.f64 x x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (fma.f64 x x x))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))
(pow.f64 (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 x) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 x) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal -2 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x #s(literal -1/2 binary64)) x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (.f64 x x) #s(literal -2 binary64)))))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (neg.f64 x)))
(/.f64 #s(literal 1/2 binary64) (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal -2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) x)))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x))) (neg.f64 (neg.f64 x)))
(pow.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x #s(literal -1/2 binary64)) x) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x))
(.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x x)) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) (*.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log1p.f64 x) (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(hypot.f64 x (sqrt.f64 x))
(hypot.f64 x (neg.f64 (sqrt.f64 x)))
(hypot.f64 (sqrt.f64 x) x)
(hypot.f64 (sqrt.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 (sqrt.f64 x)) x)
(hypot.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 x))
(hypot.f64 (neg.f64 x) (sqrt.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 (sqrt.f64 x)))
(sqrt.f64 (fma.f64 x x x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 (.f64 x x) x) (.f64 (fma.f64 x x x) (-.f64 (*.f64 x x) x)))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (fma.f64 x x (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x x) (-.f64 (.f64 x x) x))) (sqrt.f64 (-.f64 (*.f64 x x) x)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (sqrt.f64 (neg.f64 (.f64 (fma.f64 x x x) (-.f64 (.f64 x x) x)))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) x))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (sqrt.f64 (-.f64 x (*.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) x)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (sqrt.f64 (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 x x x) (-.f64 (.f64 x x) x)))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) x))))
(pow.f64 (fma.f64 x x x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (fma.f64 x x x) (fma.f64 x x x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x x))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x x) (-.f64 (.f64 x x) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x x) (-.f64 (.f64 x x) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x))))
(*.f64 (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 1/4 binary64)))

eval245.0ms (2.8%)

Memory: 10.9MiB live, 317.9MiB allocated
Compiler: Compiled 41 267 to 4 262 computations (89.7% saved)

prune252.0ms (2.9%)

Memory

9.0MiB live, 388.2MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1 560	18	1 578
Fresh	3	1	4
Picked	2	3	5
Done	0	1	1
Total	1 565	23	1 588

Accuracy

100.0%

Counts

1 588 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.8%	(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))) x (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	40.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	40.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (sqrt.f64 (.f64 x (fma.f64 x x x)))))
	40.7%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	37.5%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x))))
	39.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))))
▶	83.3%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	38.7%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	27.7%	(-.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)))))
▶	68.0%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
▶	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x))
	48.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64))))
	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))) x))
	97.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (.f64 x (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
	97.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) x)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	98.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))))
	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
✓	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
	82.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	98.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)))

Compiler

Compiled 690 to 400 computations (42% saved)

simplify131.0ms (1.5%)

Memory

1.6MiB live, 154.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	320	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
cost-diff	320	(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64))
cost-diff	384	(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x)
cost-diff	384	(/.f64 (/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x)
cost-diff	0	(sqrt.f64 (fma.f64 x x x))
cost-diff	0	(*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (+ 1 x) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
cost-diff	0	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x 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	320	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
cost-diff	384	(/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x))
cost-diff	384	(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x)))
cost-diff	2304	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))

Rules

4 558×	`lower-fma.f32`
4 556×	`lower-fma.f64`
2 284×	`lower-*.f32`
2 272×	`lower-*.f64`
1 028×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	313
0	69	311
1	117	294
2	210	273
3	363	263
4	715	263
5	2260	262
6	4582	262
7	7751	262
0	8058	258

Stop Event

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

Calls

Call 1

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

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

localize204.0ms (2.3%)

Memory

10.7MiB live, 283.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.16015625	(/.f64 (/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x)
accuracy	0.234375	(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x))
accuracy	0.0078125	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.1484375	(*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
accuracy	1.128009302813104	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
accuracy	30.72320694668863	(sqrt.f64 (fma.f64 x x x))
accuracy	0.0859375	(.f64 x (.f64 x x))
accuracy	0.13010041222651253	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	0.6492716887308647	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
accuracy	19.720584242970258	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
accuracy	0	(sqrt.f64 x)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.47227185889832	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.0234375	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.203125	(/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 x))))

Samples

129.0ms	214×	1	valid
23.0ms	37×	2	valid
1.0ms	5×	0	valid

Compiler

Compiled 268 to 33 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-div: 28.0ms (29.9% of total)

ival-mult: 17.0ms (18.2% of total)

ival-sqrt: 15.0ms (16% of total)

adjust: 14.0ms (15% of total)

ival-add: 11.0ms (11.8% of total)

ival-sub: 6.0ms (6.4% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.3%)

Memory

-11.4MiB live, 30.5MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(/ (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) x)
2.0ms	x	@	-inf	(/ (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) x)
1.0ms	x	@	-inf	(* (/ (/ -1/2 x) (sqrt x)) (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)))
1.0ms	x	@	-inf	(/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x))
1.0ms	x	@	-inf	(+ (sqrt (+ 1 x)) (sqrt x))

simplify331.0ms (3.8%)

Memory

-1.9MiB live, 321.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 648×	`lower-fma.f64`
14 648×	`lower-fma.f32`
5 652×	`lower-*.f64`
5 652×	`lower-*.f32`
5 514×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	373	3784
1	1136	3384
2	3830	3295
0	8515	3141

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 263

Calls

Call 1

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

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

rewrite276.0ms (3.1%)

Memory

-1.4MiB live, 383.1MiB allocated

Rules

4 770×	`lower-*.f32`
4 758×	`lower-*.f64`
4 154×	`lower-/.f32`
4 138×	`lower-/.f64`
3 720×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	262
0	69	260
1	265	187
2	2186	184
0	8368	183

Stop Event

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

Counts

22 → 657

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) x))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(expm1.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
(expm1.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -2 binary64)))
(expm1.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(expm1.f64 (fma.f64 #s(literal -1/2 binary64) (log.f64 x) (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(expm1.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) (.f64 #s(literal 1/2 binary64) (log.f64 x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -2 binary64)) #s(literal -1 binary64))
(neg.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(neg.f64 (/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) x)) #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) x))))
(/.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) (neg.f64 (sqrt.f64 x)))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) x) x)
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x))) #s(literal -1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (sqrt.f64 x))
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(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x x)) (sqrt.f64 (fma.f64 x x x))) (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x x)) (sqrt.f64 (fma.f64 x x x))))
(/.f64 (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 x (-.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (fma.f64 x x x)))))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x x)) (sqrt.f64 (fma.f64 x x x)))))
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))
(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) x)) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #s(literal 1 binary64))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))))) (*.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 x)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64) (*.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x)))) #s(literal -1 binary64))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))) #s(literal -1 binary64))
(/.f64 (fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))) #s(literal 1 binary64))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64) (.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64) (.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (neg.f64 (sqrt.f64 x)))) (*.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64) (.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 x))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64) (.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))) (*.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64))) (.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #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))) #s(literal 1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64) (.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (neg.f64 (sqrt.f64 x)))) (.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 (fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))) (*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x)) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x x)) (sqrt.f64 (fma.f64 x x x))) (fma.f64 x (sqrt.f64 x) (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(.f64 (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) (+.f64 x x)) (sqrt.f64 (fma.f64 x x x)))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 x) (.f64 x #s(literal -2 binary64)))))

eval210.0ms (2.4%)

Memory: 34.7MiB live, 267.3MiB allocated
Compiler: Compiled 23 193 to 2 677 computations (88.5% saved)

prune179.0ms (2%)

Memory

-18.8MiB live, 294.8MiB allocated

Pruning

22 alts after pruning (17 fresh and 5 done)

	Pruned	Kept	Total
New	1 232	12	1 244
Fresh	9	5	14
Picked	2	3	5
Done	2	2	4
Total	1 245	22	1 267

Accuracy

100.0%

Counts

1 267 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.8%	(fma.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))) x (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	40.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	69.0%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (sqrt.f64 (.f64 x (fma.f64 x x x)))))
✓	83.3%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	97.9%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
▶	7.7%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x))))
✓	38.7%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	97.2%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
	98.6%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
	98.5%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x))))
	96.9%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))))))
✓	68.0%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	97.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal -1/2 binary64)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)) x))
	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 #s(approx (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x) x))
▶	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) (.f64 x x)))
	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
▶	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
	97.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 x) (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))))) x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64))))
	82.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 545 to 322 computations (40.9% saved)

simplify171.0ms (1.9%)

Memory

-0.5MiB live, 208.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	384	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) (.f64 x x)))
cost-diff	128	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64))
cost-diff	384	(/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) (.f64 x x))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64)))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64))))
cost-diff	384	(/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x))
cost-diff	0	(+.f64 x (sqrt.f64 x))
cost-diff	0	#s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x)))
cost-diff	0	#s(approx (- (+ 1 x) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x))))
cost-diff	0	#s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.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)))) (/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
cost-diff	320	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Rules

4 758×	`lower-fma.f32`
4 756×	`lower-fma.f64`
4 388×	`lower-*.f32`
4 380×	`lower-*.f64`
1 762×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	343
0	80	339
1	132	320
2	231	308
3	380	305
4	767	305
5	2687	295
6	5565	287
0	8745	278

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

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

localize249.0ms (2.8%)

Memory

23.0MiB live, 363.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
accuracy	0.19921875	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	30.72320694668863	(sqrt.f64 (fma.f64 x x x))
accuracy	59.57677049108313	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.46484375	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) (.f64 x x)))
accuracy	10.723963737883734	(/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) (.f64 x x))
accuracy	0.015625	(*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64)))
accuracy	0.203125	(/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x))
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (sqrt.f64 x)) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64))))
accuracy	0.6822713394908877	#s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0	#s(approx (- (+ 1 x) x) #s(literal 1 binary64))
accuracy	1.128009302813104	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x))))
accuracy	59.06226566490562	#s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x)))
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.16015625	(/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
accuracy	0.6009201656153723	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
accuracy	0.6613932769226317	#s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

Samples

144.0ms	214×	1	valid
43.0ms	37×	2	valid
1.0ms	5×	0	valid

Compiler

Compiled 266 to 41 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-mult: 43.0ms (31.6% of total)

ival-div: 40.0ms (29.4% of total)

adjust: 18.0ms (13.2% of total)

ival-sqrt: 17.0ms (12.5% of total)

ival-add: 11.0ms (8.1% of total)

ival-sub: 7.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.3%)

Memory

-10.6MiB live, 27.4MiB allocated

Counts

24 → 288

Calls

Call 1

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

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

72 calls:

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

simplify350.0ms (4%)

Memory

-2.3MiB live, 412.5MiB allocated

Algorithm

1×	egg-herbie

Rules

13 764×	`lower-fma.f64`
13 764×	`lower-fma.f32`
5 814×	`lower-*.f64`
5 814×	`lower-*.f32`
4 604×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	454	3823
1	1380	3348
2	4565	3311
0	8683	3157

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 285

Calls

Call 1

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

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

rewrite236.0ms (2.7%)

Memory

18.5MiB live, 354.7MiB allocated

Rules

4 682×	`lower-/.f32`
4 664×	`lower-/.f64`
3 778×	`lower-*.f32`
3 770×	`lower-*.f64`
2 160×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	302
0	80	302
1	322	243
2	2559	236
0	8565	228

Stop Event

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

Counts

24 → 709

Calls

Call 1

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

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

eval174.0ms (2%)

Memory: 17.1MiB live, 334.2MiB allocated
Compiler: Compiled 24 152 to 3 118 computations (87.1% saved)

prune231.0ms (2.6%)

Memory

-16.0MiB live, 296.9MiB allocated

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	1 167	7	1 174
Fresh	8	4	12
Picked	3	2	5
Done	2	3	5
Total	1 180	16	1 196

Accuracy

100.0%

Counts

1 196 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.7%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	83.2%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
	98.8%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	97.9%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	7.7%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x))) (+.f64 x (sqrt.f64 x))))
	83.3%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.2%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
✓	68.0%	#s(approx (/ (- (+ 1 x) x) (* (sqrt (+ (* x x) x)) (+ (sqrt (+ 1 x)) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	82.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
	73.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 x) (*.f64 x x))))
	98.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓	98.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (- (/ 1 (sqrt x)) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 x (sqrt.f64 x))) #s(approx (/ (- (/ 1 (sqrt x)) (sqrt x)) (sqrt x)) #s(literal -1 binary64))))
	82.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 858 to 256 computations (70.2% saved)

regimes26.0ms (0.3%)

Memory

12.1MiB live, 48.4MiB allocated

Counts

47 → 1

Calls

Call 1

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

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

Calls

2 calls:

14.0ms	x
10.0ms	(-.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
98.8%	1	`x`
98.8%	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 14 to 9 computations (35.7% saved)

regimes6.0ms (0.1%)

Memory

16.0MiB live, 15.9MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
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)))))`
98.6%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	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 14 to 9 computations (35.7% saved)

regimes10.0ms (0.1%)

Memory

-59.7MiB live, 5.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

2 calls:

8.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
7.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
7.7%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes3.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
#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)))

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

Calls

2 calls:

1.0ms	x
1.0ms	(-.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
5.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
5.5%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify6.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	123
1	50	123

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.4s (16%)

Memory

35.4MiB live, 1 077.3MiB allocated

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
14 648×	`lower-fma.f64`
14 648×	`lower-fma.f32`
13 764×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	302
0	80	302
1	322	243
2	2559	236
0	8565	228
0	373	3784
1	1136	3384
2	3830	3295
0	8515	3141
0	46	262
0	69	260
1	265	187
2	2186	184
0	8368	183
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	410	3863
1	1223	3267
2	4155	3238
0	8201	3069
0	454	3823
1	1380	3348
2	4565	3311
0	8683	3157
0	42	270
0	71	250
1	307	211
2	2629	206
0	9342	204

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×	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×	node limit
1×	iter limit

Compiler

Compiled 140 to 86 computations (38.6% saved)

preprocess75.0ms (0.9%)

Memory: -10.4MiB live, 148.5MiB allocated
Compiler: Compiled 152 to 80 computations (47.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze2.0ms (0%)

sample1.9s (21.8%)

explain162.0ms (1.8%)

preprocess73.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize45.0ms (0.5%)

series6.0ms (0.1%)

simplify437.0ms (5%)

rewrite210.0ms (2.4%)

eval33.0ms (0.4%)

prune46.0ms (0.5%)

simplify182.0ms (2.1%)

localize216.0ms (2.5%)

series27.0ms (0.3%)

simplify296.0ms (3.4%)

rewrite302.0ms (3.4%)

eval245.0ms (2.8%)

prune252.0ms (2.9%)

simplify131.0ms (1.5%)

localize204.0ms (2.3%)

series24.0ms (0.3%)

simplify331.0ms (3.8%)

rewrite276.0ms (3.1%)

eval210.0ms (2.4%)

prune179.0ms (2%)

simplify171.0ms (1.9%)

localize249.0ms (2.8%)

series22.0ms (0.3%)

simplify350.0ms (4%)

rewrite236.0ms (2.7%)

eval174.0ms (2%)

prune231.0ms (2.6%)

regimes26.0ms (0.3%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

simplify6.0ms (0.1%)

soundness1.4s (16%)

preprocess75.0ms (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