Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.1s (20.6%)

Memory

-132.7MiB live, 2 793.7MiB allocated

Samples

1.4s	6 894×	1	valid
247.0ms	1 080×	2	valid
28.0ms	282×	0	valid

Precisions

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

ival-sqrt: 633.0ms (44.4% of total)

ival-div: 248.0ms (17.4% of total)

adjust: 158.0ms (11.1% of total)

const: 130.0ms (9.1% of total)

ival-sub: 97.0ms (6.8% of total)

ival-add: 87.0ms (6.1% of total)

ival-<: 26.0ms (1.8% of total)

ival->: 24.0ms (1.7% of total)

ival-and: 11.0ms (0.8% of total)

exact: 7.0ms (0.5% of total)

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

Bogosity

explain369.0ms (3.7%)

Memory

7.5MiB live, 204.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
182	1	(1.5768059634935116e+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	183	0

Confusion

	Predicted +	Predicted -
+	182	0
-	1	73

Precision

0.994535519125683

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	182	0	0
-	1	0	73

Precision?

0.994535519125683

Recall?

1.0

Freqs

test

number	freq
0	73
1	183

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

159.0ms	432×	1	valid
14.0ms	70×	2	valid
1.0ms	10×	0	valid

Compiler

Compiled 80 to 28 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 116.0ms

ival-sqrt: 82.0ms (70.6% of total)

ival-div: 14.0ms (12.1% of total)

adjust: 9.0ms (7.7% of total)

ival-add: 5.0ms (4.3% of total)

ival-sub: 5.0ms (4.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess75.0ms (0.7%)

Memory

-21.3MiB live, 16.7MiB 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: 0.3MiB live, 0.3MiB 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
▶	36.3%	(-.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

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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)

localize77.0ms (0.8%)

Memory

-13.4MiB live, 65.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.2578125	(/.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	40.76197007217791	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

46.0ms	216×	1	valid
7.0ms	35×	2	valid
0.0ms	5×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-sub: 19.0ms (45.5% of total)

ival-sqrt: 8.0ms (19.2% of total)

ival-div: 7.0ms (16.8% of total)

adjust: 4.0ms (9.6% of total)

ival-add: 2.0ms (4.8% 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

4.1MiB live, 4.1MiB 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))

simplify376.0ms (3.7%)

Memory

-20.2MiB live, 333.8MiB 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)))

rewrite222.0ms (2.2%)

Memory

-9.7MiB live, 302.4MiB 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))))

eval32.0ms (0.3%)

Memory: 26.1MiB live, 63.9MiB allocated
Compiler: Compiled 7 402 to 706 computations (90.5% saved)

prune97.0ms (1%)

Memory

-22.0MiB live, 140.0MiB allocated

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	276	10	286
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	277	10	287

Accuracy

83.8%

Counts

287 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.8%	(/.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)))
▶	36.4%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	38.8%	(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	26.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	28.6%	(-.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)))))
	38.8%	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
▶	82.8%	#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)))
	82.1%	#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))))
	60.1%	#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 330 to 198 computations (40% saved)

simplify187.0ms (1.9%)

Memory

-8.7MiB live, 272.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 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 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
cost-diff	0	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
cost-diff	0	#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 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

10 320×	`lower-fma.f32`
10 314×	`lower-fma.f64`
3 388×	`lower-*.f32`
3 382×	`lower-*.f64`
1 878×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	329
0	63	309
1	114	301
2	226	301
3	443	301
4	1046	301
5	2369	301
6	5369	301
0	8157	301

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

localize221.0ms (2.2%)

Memory

45.3MiB live, 310.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
accuracy	0.265625	(/.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	28.491850242432747	(sqrt.f64 (fma.f64 x x x))
accuracy	58.85022450948456	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.1796875	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
accuracy	28.491850242432747	(sqrt.f64 (fma.f64 x x x))
accuracy	59.99904590877439	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	1.0076055481862176	#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	40.76197007217791	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.45673956133603	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.4981117041207026	#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	0.8143543286147418	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	10.478149518492792	(/.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	23.600803803434363	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

139.0ms	216×	1	valid
27.0ms	35×	2	valid
1.0ms	5×	0	valid

Compiler

Compiled 306 to 35 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

ival-div: 28.0ms (30.2% of total)

adjust: 20.0ms (21.6% of total)

ival-sqrt: 18.0ms (19.4% of total)

ival-add: 10.0ms (10.8% of total)

ival-mult: 9.0ms (9.7% of total)

ival-sub: 8.0ms (8.6% of total)

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

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

exact: 0.0ms (0% of total)

series92.0ms (0.9%)

Memory

-11.3MiB live, 79.3MiB 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 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x))) (patch (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x 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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (-.f64 (+.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 (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 (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>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 7)))) (taylor 0 x) (#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 (/ (+ (* 1/2 (sqrt x)) (* 1/2 (* x (- (* 1/4 (sqrt x)) (sqrt x))))) (pow x 4)) (taylor 0 x) (#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 (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) (taylor 0 x) (#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 (/ (+ (* 1/2 (sqrt x)) (* x (+ (* 1/2 (sqrt (pow x 3))) (* 1/2 (- (* 1/4 (sqrt x)) (sqrt x)))))) (pow x 4)) (taylor 0 x) (#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>) () ())) ())
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#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#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 (/ 1 (pow x 3)) (taylor -inf x) (#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 (/ 1 (pow x 3)) (taylor -inf x) (#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 (/ 1 (pow x 3)) (taylor -inf x) (#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>) () ())) ())
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#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
42.0ms	x	@	inf	(sqrt (/ 1 x))
15.0ms	x	@	-inf	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
13.0ms	x	@	0	(/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x)))
2.0ms	x	@	inf	(/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x)))
1.0ms	x	@	-inf	(/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x)))

simplify337.0ms (3.4%)

Memory

18.8MiB live, 553.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 698×	`lower-fma.f64`
16 698×	`lower-fma.f32`
5 182×	`lower-*.f64`
5 182×	`lower-*.f32`
5 074×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	490	3730
1	1465	3220
2	4803	3185
0	8736	2997

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

rewrite316.0ms (3.1%)

Memory

-14.2MiB live, 466.0MiB allocated

Rules

5 422×	`lower-*.f32`
5 416×	`lower-*.f64`
3 468×	`lower-/.f32`
3 454×	`lower-/.f64`
2 790×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	245
0	63	231
1	302	188
2	2636	183
0	8750	180

Stop Event

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

Counts

21 → 771

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

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

eval248.0ms (2.5%)

Memory: 30.0MiB live, 391.0MiB allocated
Compiler: Compiled 39 245 to 4 108 computations (89.5% saved)

prune249.0ms (2.5%)

Memory

-30.1MiB live, 468.7MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	1 528	13	1 541
Fresh	5	0	5
Picked	4	1	5
Done	0	0	0
Total	1 537	14	1 551

Accuracy

100.0%

Counts

1 551 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.1%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	83.5%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
	83.6%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
	35.9%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
▶	99.2%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.1%	(/.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)))
	82.2%	(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
▶	83.6%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
	98.2%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.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))) x))
▶	60.1%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	82.0%	#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)))
▶	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 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 390 to 248 computations (36.4% saved)

simplify238.0ms (2.4%)

Memory

-3.4MiB live, 305.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x 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	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x 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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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	0	(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
cost-diff	0	#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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))
cost-diff	0	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))

Rules

14 124×	`lower-fma.f32`
14 122×	`lower-fma.f64`
2 512×	`lower--.f64`
2 512×	`lower--.f32`
2 026×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	293
0	69	287
1	106	271
2	152	271
3	185	271
4	228	271
5	379	271
6	727	271
7	2171	271
8	4733	271
0	8127	271

Stop Event

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

Calls

Call 1

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

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

localize186.0ms (1.9%)

Memory

14.1MiB live, 338.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.1796875	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
accuracy	0.26171875	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	28.491850242432747	(sqrt.f64 (fma.f64 x x x))
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.19140625	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
accuracy	1.1296410197127764	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
accuracy	28.491850242432747	(sqrt.f64 (fma.f64 x x x))
accuracy	0.0546875	(.f64 x (.f64 x x))
accuracy	0.8143543286147418	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	1.0407834659786264	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
accuracy	23.600803803434363	(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	60.45673956133603	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.0078125	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
accuracy	0.01171875	(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
accuracy	0.265625	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.2782292710224321	#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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))

Samples

98.0ms	216×	1	valid
25.0ms	35×	2	valid
2.0ms	5×	0	valid

Compiler

Compiled 266 to 36 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

ival-div: 33.0ms (36.7% of total)

ival-add: 16.0ms (17.8% of total)

adjust: 16.0ms (17.8% of total)

ival-sqrt: 13.0ms (14.4% of total)

ival-mult: 7.0ms (7.8% of total)

ival-sub: 4.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series46.0ms (0.5%)

Memory

-18.8MiB live, 18.9MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) (patch (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (patch (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) 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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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) (+ x (sqrt (+ ( x x) x)))) (sqrt (+ 1 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(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (patch (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x))) (patch (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.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 (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -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) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -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) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (- (sqrt (/ 1 x)) 1) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1/2 (* 1/8 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) #<representation binary64>) () ())) ())
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#s(alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (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 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (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 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (sqrt x)) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (sqrt x) (* 1/2 x))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))) (taylor 0 x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt x)) (taylor inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1/16 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/16 (* -1/8 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/16 (* -1/8 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/16 (* -1/8 x)) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/16 (/ 1 x)) 1/8) x) (taylor inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/16 (/ 1 x)) 1/8) x) (taylor inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (* 1/16 (/ 1 x)) 1/8) x) (taylor inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ -1/8 x) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)) (taylor -inf x) (#s(alt (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (patch (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) 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 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 (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
2.0ms	x	@	-inf	(* (sqrt (+ 1 x)) (+ x (sqrt (+ (* x x) x))))
1.0ms	x	@	0	(/ (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (sqrt (+ (* x x) x)))
1.0ms	x	@	inf	(* (sqrt (+ 1 x)) (+ x (sqrt (+ (* x x) x))))
1.0ms	x	@	-inf	(/ 1 (+ (sqrt x) (sqrt (+ 1 x))))
0.0ms	x	@	inf	(/ 1 (+ (sqrt x) (sqrt (+ 1 x))))

simplify244.0ms (2.4%)

Memory

4.6MiB live, 278.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 710×	`lower-fma.f64`
11 710×	`lower-fma.f32`
5 192×	`lower-*.f64`
5 192×	`lower-*.f32`
3 408×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	545	4034
1	1677	3482
2	5743	3452
0	8310	3246

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 249

Calls

Call 1

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

rewrite300.0ms (3%)

Memory

8.9MiB live, 324.5MiB allocated

Rules

4 756×	`lower-*.f32`
4 748×	`lower-*.f64`
4 116×	`lower-/.f32`
4 098×	`lower-/.f64`
1 946×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	232
0	69	222
1	301	186
2	2348	185
0	8721	179

Stop Event

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

Counts

21 → 741

Calls

Call 1

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

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

eval188.0ms (1.9%)

Memory: 30.7MiB live, 279.4MiB allocated
Compiler: Compiled 29 946 to 3 643 computations (87.8% saved)

prune256.0ms (2.5%)

Memory

-6.3MiB live, 416.3MiB allocated

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	1 352	9	1 361
Fresh	6	2	8
Picked	1	4	5
Done	0	1	1
Total	1 359	16	1 375

Accuracy

100.0%

Counts

1 375 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.1%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	83.5%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
	83.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	98.1%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	29.5%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) #s(approx (/ (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	82.2%	(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
✓	83.6%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	97.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
▶	96.5%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
	98.0%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
	81.9%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 x))))
	96.3%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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)))))))
✓	60.1%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	82.0%	#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)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 363 to 221 computations (39.1% saved)

simplify205.0ms (2%)

Memory

0.5MiB live, 226.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
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 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 x (sqrt.f64 x))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
cost-diff	0	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
cost-diff	0	#s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x))
cost-diff	0	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))

Rules

10 966×	`lower-fma.f32`
10 964×	`lower-fma.f64`
2 534×	`lower-*.f32`
2 528×	`lower-*.f64`
1 320×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	339
0	69	331
1	107	315
2	157	315
3	193	315
4	250	315
5	468	315
6	1023	315
7	3732	315
8	6785	315
0	8239	315

Stop Event

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

Calls

Call 1

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

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

localize158.0ms (1.6%)

Memory

12.2MiB live, 280.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.1796875	(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
accuracy	0.9608288820536399	#s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
accuracy	28.491850242432726	(sqrt.f64 (fma.f64 x x x))
accuracy	0.00390625	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
accuracy	0.265625	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.4694826918175511	#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))
accuracy	58.85022450948456	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.19140625	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
accuracy	0.4694826918175511	#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))
accuracy	1.1296410197127764	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
accuracy	0	(sqrt.f64 x)
accuracy	0.1953125	(*.f64 x (sqrt.f64 x))
accuracy	1.0407834659786264	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
accuracy	1.1179222697127764	(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
accuracy	0.0078125	(/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)
accuracy	0.265625	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.2782292710224321	#s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x))
accuracy	0.9873244121673017	#s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64))

Samples

96.0ms	233×	1	valid
5.0ms	23×	0	valid

Compiler

Compiled 270 to 33 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-div: 21.0ms (28.5% of total)

ival-add: 20.0ms (27.1% of total)

adjust: 11.0ms (14.9% of total)

ival-sqrt: 11.0ms (14.9% of total)

ival-mult: 7.0ms (9.5% of total)

ival-sub: 2.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

24.9MiB live, 24.9MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) (patch (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) (patch #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (patch #s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ ( x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))) (patch (/.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 x)) (patch (.f64 x (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (patch (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (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 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x))) (patch (/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<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 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 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 (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -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) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -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) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -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))) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (sqrt (/ 1 x)) 1) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (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)))) (taylor 0 x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/2 x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1/2 (* 1/8 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x) (taylor inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 2 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2) (taylor -inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2) (taylor -inf x) (#s(alt #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/16 (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) (patch (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1/16 (* -1/8 x)) (pow x 3)) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) (patch (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x) (taylor inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x)) (taylor -inf x) (#s(alt #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 x))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3)))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<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 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<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 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) (patch #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) #<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
0.0ms	x	@	-inf	(/ 1/2 (* x (sqrt x)))
0.0ms	x	@	-inf	(* x (sqrt x))
0.0ms	x	@	-inf	(* (sqrt (/ 1 x)) 1/2)
0.0ms	x	@	0	(* (sqrt (/ 1 x)) 1/2)
0.0ms	x	@	inf	(* (sqrt (/ 1 x)) 1/2)

simplify375.0ms (3.7%)

Memory

-32.6MiB live, 414.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 934×	`lower-fma.f64`
14 934×	`lower-fma.f32`
5 580×	`lower-*.f64`
5 580×	`lower-*.f32`
5 382×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	473	4141
1	1427	3516
2	4850	3458
0	8917	3261

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 248

Calls

Call 1

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

rewrite278.0ms (2.8%)

Memory

13.5MiB live, 407.4MiB allocated

Rules

5 164×	`lower-/.f32`
5 148×	`lower-/.f64`
4 114×	`lower-*.f32`
4 108×	`lower-*.f64`
2 554×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	267
0	69	263
1	294	230
2	2142	230
0	8417	220

Stop Event

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

Counts

21 → 531

Calls

Call 1

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

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

eval116.0ms (1.2%)

Memory: 17.8MiB live, 217.1MiB allocated
Compiler: Compiled 22 605 to 2 188 computations (90.3% saved)

prune123.0ms (1.2%)

Memory

-10.8MiB live, 225.7MiB allocated

Pruning

18 alts after pruning (11 fresh and 7 done)

	Pruned	Kept	Total
New	1 022	7	1 029
Fresh	2	4	6
Picked	3	2	5
Done	0	5	5
Total	1 027	18	1 045

Accuracy

100.0%

Counts

1 045 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(/.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	83.5%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
	83.6%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.0%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
	29.5%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) #s(approx (/ (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.2%	(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))
✓	83.6%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	97.4%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
	96.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
	7.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
	98.0%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
✓	96.5%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
	60.0%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
	96.3%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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)))))))
✓	60.1%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	82.0%	#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)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 760 to 248 computations (67.4% saved)

regimes24.0ms (0.2%)

Memory

-7.5MiB live, 30.6MiB allocated

Counts

40 → 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.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)))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.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)))))
(-.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 x))))
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x 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))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) #s(approx (/ (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x 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)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.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))) x))
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
#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)))

Outputs

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

Calls

2 calls:

14.0ms	x
8.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	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)

regimes17.0ms (0.2%)

Memory

22.1MiB live, 22.1MiB allocated

Counts

32 → 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.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)))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.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)))))
(-.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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 x))))
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x 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))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) #s(approx (/ (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) #s(literal 1/16 binary64)) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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)))

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

Calls

2 calls:

9.0ms	x
7.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.9%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
98.9%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes23.0ms (0.2%)

Memory

-40.4MiB live, 12.5MiB allocated

Counts

17 → 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.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)))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
(/.f64 #s(approx (/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))

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

Calls

2 calls:

18.0ms	x
4.0ms	(-.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
98.2%	1	`x`
98.2%	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)

regimes9.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Counts

15 → 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.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)))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #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) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.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:

5.0ms	x
4.0ms	(-.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
98.1%	1	`x`
98.1%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes7.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

10 → 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(approx (+ 1/2 (/ (+ -1/8 (/ 1/16 x)) x)) #s(literal 1/2 binary64)) x)) #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))

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

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	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)

regimes5.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB 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(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.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 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x)))))

Outputs
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 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
96.5%	1	`x`
96.5%	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)

regimes4.0ms (0%)

Memory

5.4MiB live, 5.4MiB 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(literal 1 binary64) (*.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))

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

Calls

2 calls:

2.0ms	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
7.6%	1	`x`
7.6%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes13.0ms (0.1%)

Memory

-32.5MiB live, 5.3MiB 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:

11.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
1.0ms	x

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)

simplify7.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
6×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	195
1	67	195

Stop Event

1×

saturated

Calls

Call 1

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

soundness2.2s (21.5%)

Memory

30.5MiB live, 970.9MiB allocated

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
16 698×	`lower-fma.f64`
16 698×	`lower-fma.f32`
14 934×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416
0	490	3730
1	1465	3220
2	4803	3185
0	8736	2997
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	46	267
0	69	263
1	294	230
2	2142	230
0	8417	220
0	46	232
0	69	222
1	301	186
2	2348	185
0	8721	179
0	545	4034
1	1677	3482
2	5743	3452
0	8310	3246
0	473	4141
1	1427	3516
2	4850	3458
0	8917	3261
0	37	245
0	63	231
1	302	188
2	2636	183
0	8750	180

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

Compiler

Compiled 306 to 163 computations (46.7% saved)

preprocess65.0ms (0.7%)

Memory: 4.8MiB live, 161.1MiB allocated
Compiler: Compiled 242 to 108 computations (55.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze2.0ms (0%)

sample2.1s (20.6%)

explain369.0ms (3.7%)

preprocess75.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.1%)

localize77.0ms (0.8%)

series6.0ms (0.1%)

simplify376.0ms (3.7%)

rewrite222.0ms (2.2%)

eval32.0ms (0.3%)

prune97.0ms (1%)

simplify187.0ms (1.9%)

localize221.0ms (2.2%)

series92.0ms (0.9%)

simplify337.0ms (3.4%)

rewrite316.0ms (3.1%)

eval248.0ms (2.5%)

prune249.0ms (2.5%)

simplify238.0ms (2.4%)

localize186.0ms (1.9%)

series46.0ms (0.5%)

simplify244.0ms (2.4%)

rewrite300.0ms (3%)

eval188.0ms (1.9%)

prune256.0ms (2.5%)

simplify205.0ms (2%)

localize158.0ms (1.6%)

series13.0ms (0.1%)

simplify375.0ms (3.7%)

rewrite278.0ms (2.8%)

eval116.0ms (1.2%)

prune123.0ms (1.2%)

regimes24.0ms (0.2%)

regimes17.0ms (0.2%)

regimes23.0ms (0.2%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes13.0ms (0.1%)

simplify7.0ms (0.1%)

soundness2.2s (21.5%)

preprocess65.0ms (0.7%)

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