Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

3.2MiB live, 3.2MiB 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)

sample2.3s (27.1%)

Memory

18.5MiB live, 1 876.9MiB allocated

Samples

1.5s	6 890×	1	valid
264.0ms	1 084×	2	valid
21.0ms	282×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-div: 358.0ms (23.5% of total)

ival-add: 282.0ms (18.5% of total)

ival-sqrt: 281.0ms (18.5% of total)

const: 208.0ms (13.7% of total)

adjust: 178.0ms (11.7% of total)

ival-sub: 143.0ms (9.4% of total)

ival->: 32.0ms (2.1% of total)

ival-<: 19.0ms (1.2% of total)

ival-and: 12.0ms (0.8% of total)

exact: 7.0ms (0.5% of total)

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

Bogosity

explain211.0ms (2.5%)

Memory

-2.0MiB live, 115.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
173	1	(2.3710520403633864e+215)	1	(18.510883862284683)	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	0	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	0	-	`(sqrt.f64 x)`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	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	173	2

Confusion

	Predicted +	Predicted -
+	172	2
-	1	81

Precision

0.9942196531791907

Recall

0.9885057471264368

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	172	2	0
-	1	0	81

Precision?

0.9942857142857143

Recall?

1.0

Freqs

test

number	freq
0	83
1	173

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

107.0ms	436×	1	valid
11.0ms	58×	2	valid
1.0ms	18×	0	valid

Compiler

Compiled 79 to 28 computations (64.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-add: 35.0ms (44.9% of total)

ival-sqrt: 15.0ms (19.2% of total)

ival-div: 13.0ms (16.7% of total)

adjust: 9.0ms (11.5% of total)

ival-sub: 5.0ms (6.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess22.0ms (0.3%)

Memory

8.7MiB live, 8.7MiB 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 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify9.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB 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 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))

localize68.0ms (0.8%)

Memory

-21.8MiB live, 31.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.3671875	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.37109375	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	38.24439415243994	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

28.0ms	218×	1	valid
6.0ms	29×	2	valid
1.0ms	9×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 8.0ms (33.6% of total)

ival-div: 7.0ms (29.4% of total)

adjust: 5.0ms (21% of total)

ival-sub: 2.0ms (8.4% of total)

ival-add: 2.0ms (8.4% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
2.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))
1.0ms	x	@	0	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))) (sqrt (+ x 1)))

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify176.0ms (2.1%)

Memory

34.6MiB live, 144.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16 898×	`lower-fma.f64`
16 898×	`lower-fma.f32`
5 002×	`lower-*.f64`
5 002×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite199.0ms (2.4%)

Memory

-1.0MiB live, 161.0MiB 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	27
0	14	27
1	66	23
2	565	23
3	6719	23
0	8113	23

Stop Event

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

Counts

5 → 285

Calls

Call 1

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

Outputs
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eval72.0ms (0.9%)

Memory: 1.9MiB live, 83.8MiB allocated
Compiler: Compiled 7 270 to 957 computations (86.8% saved)

prune68.0ms (0.8%)

Memory

-28.2MiB live, 49.3MiB allocated

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	329	16	345
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	329	17	346

Accuracy

85.3%

Counts

346 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.0%	(fma.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (pow.f64 x #s(literal -1/2 binary64)))
	40.2%	(/.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
▶	42.8%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	42.8%	(/.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	42.8%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x))))
▶	42.8%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓	40.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	5.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
▶	36.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x))))
	3.5%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))))
	25.7%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	28.9%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	84.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
▶	84.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	70.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
▶	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 543 to 370 computations (31.9% saved)

simplify265.0ms (3.2%)

Memory

18.9MiB live, 177.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 (sqrt.f64 x) x)
cost-diff	0	(*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	128	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
cost-diff	320	(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	768	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))
cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
cost-diff	320	(fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

Rules

11 632×	`lower-fma.f32`
11 622×	`lower-fma.f64`
2 924×	`lower-*.f32`
2 914×	`lower-*.f64`
2 232×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	432
0	91	427
1	167	427
2	435	405
3	1527	402
4	5921	401
0	8268	397

Stop Event

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

Calls

Call 1

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

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

localize288.0ms (3.4%)

Memory

-2.0MiB live, 476.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.16015625	(*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	0.8376610752105884	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
accuracy	58.129869787654435	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.203125	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
accuracy	0.3671875	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
accuracy	0.5	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	58.129869787654435	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.3671875	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.37109375	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))
accuracy	1.506528339007633	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy	38.24439415243994	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.32272381930191	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.7016859436769535	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
accuracy	9.501652805379868	(/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
accuracy	12.669988215950788	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))
accuracy	17.493987140381442	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))

Samples

169.0ms	218×	1	valid
57.0ms	29×	2	valid
3.0ms	9×	0	valid

Compiler

Compiled 420 to 48 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 190.0ms

adjust: 55.0ms (29% of total)

ival-mult: 35.0ms (18.5% of total)

ival-hypot: 31.0ms (16.3% of total)

ival-div: 26.0ms (13.7% of total)

ival-add: 14.0ms (7.4% of total)

ival-sqrt: 13.0ms (6.9% of total)

ival-pow: 5.0ms (2.6% of total)

ival-sub: 4.0ms (2.1% of total)

ival-neg: 4.0ms (2.1% of total)

exact: 1.0ms (0.5% of total)

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

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

series34.0ms (0.4%)

Memory

4.2MiB live, 84.2MiB allocated

Counts

24 → 288

Calls

Call 1

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

Outputs
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#s(alt (/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))))) (pow x 3)) (taylor 0 x) (#s(alt (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 (sqrt x)) (sqrt x)))) (pow x 3)) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (+ (* -1/4 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (sqrt x)))) (pow x 3)) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (+ (* 1/2 (sqrt x)) (* x (- (* -1 (sqrt (pow x 3))) (* 1/4 (sqrt x))))) (sqrt x)))) (pow x 3)) (taylor 0 x) (#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (pow x 5))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
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#s(alt (/ 1 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))) (patch (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) (patch (/.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 3)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

9.0ms

-inf

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

7.0ms

inf

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

6.0ms

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

simplify220.0ms (2.6%)

Memory

5.6MiB live, 287.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 756×	`lower-fma.f64`
10 756×	`lower-fma.f32`
6 038×	`lower-*.f64`
6 038×	`lower-*.f32`
3 762×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	646	4800
1	2003	4039
2	6931	4035
0	8089	3822

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 285

Calls

Call 1

Inputs
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (* x (- (* 1/2 (sqrt x)) (sqrt x))))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))))) (pow x 3))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* x (- (* 1/2 (sqrt x)) (sqrt x)))) (pow x 3))
(/ (+ (sqrt x) (* x (- (+ (* -1/4 (sqrt (pow x 3))) (* 1/2 (sqrt x))) (sqrt x)))) (pow x 3))
(/ (+ (sqrt x) (* x (- (+ (* 1/2 (sqrt x)) (* x (- (* -1 (sqrt (pow x 3))) (* 1/4 (sqrt x))))) (sqrt x)))) (pow x 3))
(sqrt (/ 1 (pow x 5)))
(sqrt (/ 1 (pow x 5)))
(sqrt (/ 1 (pow x 5)))
(sqrt (/ 1 (pow x 5)))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(* -1 (+ 1 (sqrt x)))
(+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (* x (+ 1/8 (* -1/8 (+ 1 (sqrt x)))))) (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))) (* x (+ (* -1 (* x (- (* 1/16 (+ 1 (sqrt x))) 1/16))) (* -1 (+ 1/8 (* -1/8 (+ 1 (sqrt x))))))))))
1
1
1
1
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(* (sqrt x) (+ 1 (sqrt x)))
(+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))))))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))) (* x (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))))))) (* (sqrt x) (+ 1 (sqrt x))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* -1/2 (sqrt (/ 1 (pow x 9))))
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (* x (- (* 1/2 (sqrt x)) (sqrt x))))) (pow x 5))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))))) (pow x 5))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))))) (pow x 5))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* -1 (sqrt (/ 1 x)))
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(* -2 x)
(* -1 (* (pow x 2) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (pow x 2))))))
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(* (pow x 2) (- (+ (* -1 (/ (- (* 3/16 (pow x 2)) (* 1/8 (pow x 2))) (pow x 6))) (* 1/8 (/ 1 (pow x 3)))) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (pow x 2))))))
1
1
1
1
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(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
x
(* x (+ 1 (/ 1 x)))
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(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* 2 (sqrt (/ 1 x)))))
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(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/8 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
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(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (/ (- (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x))) (pow x 2))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (+ (* -1/2 (/ (- (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x))) (pow x 2))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))) x)
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(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
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(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
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(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
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(* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
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(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(+ (* -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))))
(* 2 (* x (pow (sqrt -1) 2)))
(* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (pow x 2))))))
1
1
1
1
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 8))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) x)) (* 1/2 (pow (sqrt -1) 2))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)))))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 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)))))))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* -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))))))))

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

rewrite161.0ms (1.9%)

Memory

11.9MiB live, 243.5MiB allocated

Rules

4 144×	`lower-fma.f32`
4 134×	`lower-fma.f64`
3 344×	`lower-*.f32`
3 334×	`lower-*.f64`
3 286×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	315
0	91	298
1	388	246
2	3379	246
0	8491	246

Stop Event

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

Counts

24 → 1 058

Calls

Call 1

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

Outputs
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eval285.0ms (3.4%)

Memory: -8.0MiB live, 582.7MiB allocated
Compiler: Compiled 56 490 to 5 597 computations (90.1% saved)

prune58.0ms (0.7%)

Memory

-15.3MiB live, 152.5MiB allocated

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	2 008	19	2 027
Fresh	7	4	11
Picked	4	1	5
Done	0	1	1
Total	2 019	25	2 044

Accuracy

100.0%

Counts

2 044 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.8%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	42.8%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	41.8%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (.f64 #s(approx (sqrt (+ ( (sqrt x) (sqrt x)) (* x x))) (+.f64 #s(literal 1/2 binary64) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	37.4%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
	42.8%	(/.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (pow.f64 (fma.f64 x x x) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	40.4%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)))
	99.2%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
▶	98.6%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
▶	99.4%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓	40.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	5.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
	28.9%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	42.8%	(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (/.f64 (neg.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x)) (sqrt.f64 x)))
	84.1%	#s(approx (/ (- (+ x 1) x) (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1))))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64) (fma.f64 #s(literal 3/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (.f64 x x)))
	70.0%	#s(approx (/ (- (+ x 1) x) (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
	98.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64) (pow.f64 x #s(literal -5/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) x))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (/.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64) (pow.f64 x #s(literal -5/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x) (sqrt.f64 x)) (sqrt.f64 x)))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
	97.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64) (pow.f64 x #s(literal -5/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x))))
▶	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	85.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (-.f64 (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64) (pow.f64 x #s(literal -5/2 binary64))) (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))) #s(literal -1/2 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal -2 binary64))))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	82.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (.f64 x x))))
✓	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	97.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))

Compiler

Compiled 870 to 583 computations (33% saved)

simplify124.0ms (1.5%)

Memory

33.4MiB live, 104.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 (sqrt.f64 x) x)
cost-diff	0	(*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
cost-diff	0	(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
cost-diff	1536	(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)))
cost-diff	320	(*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
cost-diff	384	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
cost-diff	0	#s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
cost-diff	768	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Rules

11 880×	`lower-fma.f32`
11 878×	`lower-fma.f64`
3 324×	`lower-*.f32`
3 314×	`lower-*.f64`
2 158×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	438
0	106	434
1	182	434
2	425	380
3	1331	376
4	4717	372
0	8343	364

Stop Event

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

Calls

Call 1

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

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

localize245.0ms (2.9%)

Memory

-18.3MiB live, 307.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.0234375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.16015625	(*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	0.8376610752105884	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
accuracy	0.19140625	(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
accuracy	0.203125	(/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x)
accuracy	0.7016859436769535	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
accuracy	1.628455128220357	#s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #s(literal 5/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x))
accuracy	0.203125	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)))
accuracy	0.3671875	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
accuracy	1.5394927278608193	#s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x))
accuracy	58.129869787654435	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.3671875	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.32272381930191	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.0234375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.203125	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
accuracy	0.5	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

161.0ms	218×	1	valid
30.0ms	29×	2	valid
3.0ms	9×	0	valid

Compiler

Compiled 354 to 57 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 157.0ms

ival-div: 43.0ms (27.4% of total)

ival-mult: 29.0ms (18.5% of total)

adjust: 24.0ms (15.3% of total)

ival-add: 20.0ms (12.8% of total)

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

ival-hypot: 9.0ms (5.7% of total)

ival-neg: 7.0ms (4.5% of total)

ival-sub: 5.0ms (3.2% of total)

ival-pow: 5.0ms (3.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series25.0ms (0.3%)

Memory

-15.1MiB live, 24.9MiB allocated

Counts

25 → 300

Calls

Call 1

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

Outputs
#s(alt (* -1 (+ 1 (sqrt x))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (* x (+ 1/8 (* -1/8 (+ 1 (sqrt x)))))) (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))) (* x (+ (* -1 (* x (- (* 1/16 (+ 1 (sqrt x))) 1/16))) (* -1 (+ 1/8 (* -1/8 (+ 1 (sqrt x)))))))))) (taylor 0 x) (#s(alt (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (patch (/.f64 #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (patch #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (patch (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (patch (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (patch (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (patch (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor 0 x) (#s(alt (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (patch (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 8))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (patch (.f64 (hypot.f64 (sqrt.f64 x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (hypot.f64 (sqrt.f64 x) x) (patch (hypot.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) x))))) (taylor -inf x) (#s(alt (hypot.f64 (sqrt.f64 x) x) (patch (hypot.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) x)) (* 1/2 (pow (sqrt -1) 2))) x))))) (taylor -inf x) (#s(alt (hypot.f64 (sqrt.f64 x) x) (patch (hypot.f64 (sqrt.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x))))) (taylor -inf x) (#s(alt (hypot.f64 (sqrt.f64 x) x) (patch (hypot.f64 (sqrt.f64 x) 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>) () ())) ())
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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 x #s(literal 1 binary64)))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (.f64 #s(literal -2 binary64) x)) (patch #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (patch (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (patch (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (patch (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) (patch (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

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

3.0ms

-inf

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

2.0ms

inf

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

simplify156.0ms (1.9%)

Memory

39.6MiB live, 147.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 004×	`lower-fma.f64`
11 004×	`lower-fma.f32`
5 814×	`lower-*.f64`
5 814×	`lower-*.f32`
3 228×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	567	4875
1	1751	4093
2	5957	4049
0	8359	3836

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 297

Calls

Call 1

Inputs
(* -1 (+ 1 (sqrt x)))
(+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (* x (+ 1/8 (* -1/8 (+ 1 (sqrt x)))))) (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))))))
(+ (* -1 (+ 1 (sqrt x))) (* x (+ (* -1 (+ 1/2 (* 1/2 (+ 1 (sqrt x))))) (* x (+ (* -1 (* x (- (* 1/16 (+ 1 (sqrt x))) 1/16))) (* -1 (+ 1/8 (* -1/8 (+ 1 (sqrt x))))))))))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
1
1
1
1
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(* 5/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* -1/2 (sqrt (/ 1 (pow x 9))))
(/ (+ (* -1/2 (sqrt x)) (* -1/2 (* x (- (* 1/2 (sqrt x)) (sqrt x))))) (pow x 5))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (* 1/8 (sqrt x))))))) (pow x 5))
(/ (+ (* -1/2 (sqrt x)) (* x (+ (* -1/2 (- (* 1/2 (sqrt x)) (sqrt x))) (* x (+ (* -1/2 (sqrt x)) (+ (* 1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3))))))))) (pow x 5))
(* 5/8 (sqrt (/ 1 (pow x 5))))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(/ (+ (* 1/2 (sqrt (pow x 3))) (* 5/8 (sqrt x))) (pow x 3))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
1
1
1
1
(* (sqrt x) (+ 1 (sqrt x)))
(+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))))))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))) (* x (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))))))) (* (sqrt x) (+ 1 (sqrt x))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* -1 (+ 1 (sqrt x)))
(+ (* -1 (* x (+ 1/2 (* 1/2 (+ 1 (sqrt x)))))) (* -1 (+ 1 (sqrt x))))
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(* -1 (sqrt (/ 1 x)))
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(* -1 (sqrt (/ 1 x)))
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(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
1
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(* 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))
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(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
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1
1
1
1
(* -1 (sqrt (/ 1 x)))
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(/ (+ (* -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))
x
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(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3)))))
(+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3)))))
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(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (/ (- (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x))) (pow x 2))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 7)))) (+ (* -1/2 (/ (- (* 1/2 (sqrt (/ 1 x))) (sqrt (/ 1 x))) (pow x 2))) (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
(/ (+ (* 1/2 (sqrt (/ 1 x))) (* 5/8 (sqrt (/ 1 (pow x 3))))) x)
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(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
1
1
1
1
(* 2 (sqrt (pow x 3)))
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(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/8 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
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(sqrt (/ 1 x))
(sqrt (/ 1 x))
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(* -2 x)
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(* (pow x 2) (- (+ (* -1 (/ (- (* 3/16 (pow x 2)) (* 1/8 (pow x 2))) (pow x 6))) (* 1/8 (/ 1 (pow x 3)))) (+ (* 2 (/ 1 x)) (* 3/2 (/ 1 (pow x 2))))))
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(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 2 (* x (pow (sqrt -1) 2)))
(* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (pow x 2))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
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(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
1
1
1
1
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x)) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -5/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
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(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
1
1
1
1
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 8))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ (pow (sqrt -1) 2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 4) x)) (* 1/2 (pow (sqrt -1) 2))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 4)) (* -1/16 (/ (pow (sqrt -1) 6) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* -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))))))))
(* 2 (* x (pow (sqrt -1) 2)))
(* (pow x 2) (- (* 2 (/ (pow (sqrt -1) 2) x)) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (* 3/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* -1 (/ (- (* -1/4 (/ x (pow (sqrt -1) 2))) (* -3/8 (/ x (pow (sqrt -1) 2)))) (pow x 4))) (* 2 (/ (pow (sqrt -1) 2) x))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 3/2 (/ 1 (pow x 2))))))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

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

rewrite169.0ms (2%)

Memory

7.5MiB live, 166.1MiB allocated

Rules

4 218×	`lower-fma.f32`
4 216×	`lower-fma.f64`
3 442×	`lower-*.f32`
3 432×	`lower-*.f64`
3 232×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	377
0	106	360
1	411	320
2	3375	320
0	8514	314

Stop Event

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

Counts

25 → 736

Calls

Call 1

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

Outputs
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eval260.0ms (3.1%)

Memory: -19.4MiB live, 257.8MiB allocated
Compiler: Compiled 34 674 to 4 832 computations (86.1% saved)

prune48.0ms (0.6%)

Memory

-14.9MiB live, 111.9MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1 583	14	1 597
Fresh	13	5	18
Picked	3	2	5
Done	0	2	2
Total	1 599	23	1 622

Accuracy

100.0%

Counts

1 622 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	37.4%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
	41.8%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 x x) #s(literal -3/2 binary64))))
	40.4%	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)) (.f64 #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)) (sqrt.f64 x)))
	97.2%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)))
	97.5%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (.f64 (hypot.f64 (sqrt.f64 x) x) #s(approx (+ (sqrt x) (sqrt (+ x 1))) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))))
	98.5%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (.f64 (.f64 (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) (pow.f64 x #s(literal 1/4 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	85.1%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	97.6%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (sqrt x) (sqrt x)) (* x x))) (+.f64 #s(literal 1/2 binary64) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
▶	8.0%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
▶	99.4%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
✓	99.4%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	84.1%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (* (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (fma.f64 (/.f64 #s(literal -2 binary64) x) (*.f64 x x) #s(literal -3/2 binary64))))
✓	40.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	5.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
	99.1%	(.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(approx ( (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
	70.0%	#s(approx (/ (- (+ x 1) x) (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	82.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (.f64 x x))))
✓	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	97.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* (sqrt (/ 1 x)) 1/2)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
	96.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 5/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))

Compiler

Compiled 633 to 473 computations (25.3% saved)

simplify187.0ms (2.2%)

Memory

35.6MiB live, 187.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
cost-diff	0	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
cost-diff	0	(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (.f64 x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) 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) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
cost-diff	0	(+.f64 (sqrt.f64 x) x)
cost-diff	0	#s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
cost-diff	0	#s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
cost-diff	0	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
cost-diff	128	(+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
cost-diff	1920	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Rules

26 952×	`lower-fma.f32`
26 950×	`lower-fma.f64`
3 872×	`lower-*.f32`
3 864×	`lower-*.f64`
1 844×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	401
0	80	381
1	139	372
2	264	330
3	604	330
4	1429	324
5	4513	324
0	8851	314

Stop Event

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

Calls

Call 1

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

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

localize252.0ms (3%)

Memory

-36.9MiB live, 206.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.1796875	(/.f64 (/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	0.30306625976844204	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
accuracy	0.3671875	(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
accuracy	0.0078125	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	1.248773173520451	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (.f64 x x))))
accuracy	9.535740314763713	(/.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 x x))
accuracy	0.3671875	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.3671875	(/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
accuracy	38.24048790243994	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))))
accuracy	59.27929446918639	#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
accuracy	0.8376610752105884	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
accuracy	58.685784317815774	#s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))
accuracy	0.1328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.19921875	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
accuracy	0.49609375	(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	0.515625	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Samples

166.0ms	218×	1	valid
47.0ms	29×	2	valid
2.0ms	8×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 334 to 40 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-div: 45.0ms (29.8% of total)

ival-sqrt: 36.0ms (23.8% of total)

adjust: 18.0ms (11.9% of total)

ival-add: 18.0ms (11.9% of total)

ival-mult: 16.0ms (10.6% of total)

ival-hypot: 9.0ms (6% of total)

ival-sub: 7.0ms (4.6% of total)

ival-neg: 2.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.3%)

Memory

36.0MiB live, 36.0MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

-inf

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

3.0ms

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

3.0ms

inf

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

simplify169.0ms (2%)

Memory

-31.1MiB live, 125.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 570×	`lower-fma.f64`
8 570×	`lower-fma.f32`
5 076×	`lower-*.f64`
5 076×	`lower-*.f32`
3 830×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	695	4654
1	2106	3895
2	7348	3856
0	8036	3686

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

Inputs
-1
(- (* -1 x) 1)
(- (* -1 x) 1)
(- (* -1 x) 1)
(- (* -1 (sqrt x)) 1)
(- (+ (* -1 x) (* -1 (sqrt x))) 1)
(- (+ (* -1 (sqrt x)) (* x (- (* -1/2 (sqrt x)) 1))) 1)
(- (+ (* -1 (sqrt x)) (* x (- (* x (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (sqrt x)))) 1))) 1)
(* -1 (* (sqrt (/ 1 x)) (/ 1 (- (* -1 (sqrt x)) 1))))
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* x (+ (* -1 (* (sqrt x) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))) (* -1 (* (sqrt (pow x 3)) (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))))))))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (- (* -1 (sqrt x)) 1)))) (* x (+ (* -1 (* (sqrt x) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2)))) (* x (+ (* -1 (* (sqrt x) (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))))) (* (sqrt (pow x 3)) (+ (* -1 (/ (- (/ 1 (pow (- (* -1 (sqrt x)) 1) 3)) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 2))))) (- (* -1 (sqrt x)) 1))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (pow (- (* -1 (sqrt x)) 1) 3))))))))))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
1
1
1
1
(* (sqrt x) (+ 1 (sqrt x)))
(+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))))))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (+ (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (sqrt x)))) (* x (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt (/ 1 x)))))))))) (* (sqrt x) (+ 1 (sqrt x))))
(sqrt x)
(+ x (sqrt x))
(+ x (sqrt x))
(+ x (sqrt x))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 (pow x 5)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 3))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -1 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))
(/ (+ (* -1 (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) (* 1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2))))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) (* x (+ (* -1 (* (sqrt (pow x 3)) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2))))))) x)
(/ (+ (* -1 (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) (* x (+ (* 1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1 (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* (sqrt (pow x 3)) (+ (* 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)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))))))))))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt x))
(+ (* -1 (sqrt x)) (* -1/2 (sqrt (pow x 3))))
(+ (* -1 (sqrt x)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* 1/8 (sqrt x)))))
(+ (* -1 (sqrt x)) (* (pow x 2) (+ (* -1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/8 (sqrt (/ 1 (pow x 3)))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -2 x)
(* -1 (* x (+ 2 (* 3/2 (/ 1 x)))))
(* x (- (/ 1/8 (pow x 2)) (+ 2 (* 3/2 (/ 1 x)))))
(* x (- (/ 1/8 (pow x 2)) (+ 2 (+ (* 3/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (+ (* -35/128 (sqrt (/ 1 (pow x 7)))) (+ (* 5/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
1
1
1
1
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/8 (sqrt (/ 1 (pow x 7)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))))
(* x (+ 1 (sqrt (/ 1 x))))
(* x (+ 1 (sqrt (/ 1 x))))
(* x (+ 1 (sqrt (/ 1 x))))
(* x (+ 1 (sqrt (/ 1 x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 x)) 1/2) x)
(/ (- (/ 1/8 x) (+ 1/2 (* 1/16 (/ 1 (pow x 2))))) x)
(/ (- (+ (* (sqrt (/ 1 (pow x 13))) (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7))))) (/ 1/8 x)) (+ 1/2 (* 1/16 (/ 1 (pow x 2))))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* x (- (/ 1/8 (pow x 2)) (+ 1 (* 1/2 (/ 1 x)))))
(* x (- (/ 1/8 (pow x 2)) (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3)))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -1 x)
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (/ 1 x))))
(* -1 (* x (+ 1 (* -1 (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1 (+ (* -1 (pow (sqrt -1) 2)) (* 3/2 (/ 1 x))))))
(* -1 (* x (+ 1 (+ (* -1 (pow (sqrt -1) 2)) (+ (/ 1/8 (* (pow x 2) (pow (sqrt -1) 2))) (* 3/2 (/ 1 x)))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (- (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 3/2) x)) (* -1 (pow (sqrt -1) 2))))))
(* (sqrt (/ 1 (pow x 3))) (/ 1 (+ 1 (* -1 (pow (sqrt -1) 2)))))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (* -1 (pow (sqrt -1) 2)))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2))))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (* -1 (pow (sqrt -1) 2)))))) (* -1 (/ (+ (* -3/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2)))) (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- (* 9/4 (/ 1 (* (sqrt -1) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt -1) 3) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2)))))))) x))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (* -1 (pow (sqrt -1) 2)))))) (* -1 (/ (+ (* -3/2 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2)))) (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (- (* 9/4 (/ 1 (* (sqrt -1) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt -1) 3) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2)))))))) (* (sqrt (/ 1 (pow x 3))) (* (sqrt -1) (- (* 1/16 (/ 1 (* (pow (sqrt -1) 5) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2)))) (+ (* -3/2 (/ (- (* 9/4 (/ 1 (* (sqrt -1) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 3)))) (* 1/8 (/ 1 (* (pow (sqrt -1) 3) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 2))))) (+ 1 (* -1 (pow (sqrt -1) 2))))) (* 3/16 (/ 1 (* (pow (sqrt -1) 3) (pow (+ 1 (* -1 (pow (sqrt -1) 2))) 3))))))))) x))) x))) x))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (+ (* 1/2 (* (pow (sqrt -1) 2) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (pow (sqrt -1) 6)))) (* 1/16 (sqrt (pow x 3)))) x)) (+ (* -1/4 (* (sqrt x) (+ (* -1 (pow (sqrt -1) 4)) (* 1/4 (pow (sqrt -1) 4))))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (* 1/2 (sqrt x))) (pow x 2))
1
1
1
1
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 8))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2)))) x)) (+ (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 6))) (* 1/2 (sqrt x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 4))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (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 (pow x 3))) (pow (sqrt -1) 2))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (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))
(/ 1/2 (* x (pow (sqrt -1) 2)))
(/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x)
(* -1 (/ (- (/ -1/8 (* x (pow (sqrt -1) 4))) (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 13))) (* (sqrt -1) (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7))))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* -1 (sqrt (/ 1 x)))
(* x (pow (sqrt -1) 2))
(* -1 (* x (+ (* -1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (pow (sqrt -1) 2)) (+ (/ 1/8 (* (pow x 2) (pow (sqrt -1) 2))) (* 1/2 (/ 1 x))))))
(* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x)) 1/2) x)) (* -1 (pow (sqrt -1) 2)))))
(* -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)))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* -2 (* (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))))))))

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

rewrite151.0ms (1.8%)

Memory

41.6MiB live, 157.4MiB allocated

Rules

4 632×	`lower-*.f32`
4 624×	`lower-*.f64`
4 154×	`lower-fma.f32`
4 152×	`lower-fma.f64`
3 084×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	321
0	80	299
1	353	273
2	2802	267
0	8206	255

Stop Event

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

Counts

23 → 524

Calls

Call 1

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

Outputs
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eval173.0ms (2.1%)

Memory: -8.7MiB live, 182.8MiB allocated
Compiler: Compiled 21 220 to 2 932 computations (86.2% saved)

prune53.0ms (0.6%)

Memory

-17.1MiB live, 76.4MiB allocated

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	1 013	7	1 020
Fresh	7	7	14
Picked	4	1	5
Done	1	3	4
Total	1 025	18	1 043

Accuracy

100.0%

Counts

1 043 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	37.4%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
	97.2%	(/.f64 (.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) #s(approx ( (+ (sqrt x) (sqrt (+ x 1))) (neg (sqrt (+ x 1)))) (*.f64 #s(literal -2 binary64) x)))
	98.7%	(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.5%	(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	85.1%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	97.6%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (.f64 #s(approx (sqrt (+ ( (sqrt x) (sqrt x)) (* x x))) (+.f64 #s(literal 1/2 binary64) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
✓	8.0%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
	99.5%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (/.f64 (sqrt.f64 x) x))) (+.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
	99.7%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (+.f64 x #s(literal 1 binary64)))))
	98.7%	(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (+ (* (sqrt (+ 1 x)) (neg (sqrt (+ 1 x)))) (* (sqrt x) (neg (sqrt (+ 1 x))))) (fma.f64 #s(literal -2 binary64) x #s(literal -3/2 binary64))))
✓	40.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (-.f64 (pow.f64 x #s(literal -5/2 binary64)) (pow.f64 x #s(literal -3/2 binary64))) #s(literal -1/2 binary64)))
	74.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (pow.f64 x #s(literal 3/2 binary64))))))
✓	5.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	97.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* (sqrt (/ 1 x)) 1/2)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
	96.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 5/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))))))

Compiler

Compiled 1 211 to 410 computations (66.1% saved)

regimes39.0ms (0.5%)

Memory

-10.9MiB live, 27.2MiB allocated

Counts

57 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

24.0ms	x
12.0ms	(-.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
99.7%	1	`x`
99.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes15.0ms (0.2%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

8.0ms	x
6.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

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

Compiler

Compiled 12 to 9 computations (25% saved)

regimes15.0ms (0.2%)

Memory

6.1MiB live, 38.2MiB allocated

Counts

18 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

9.0ms	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
98.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
98.7%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
97.5%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.1%)

Memory

-34.6MiB live, 11.8MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

9.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
97.3%	1	`x`
97.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
82.8%	1	`x`
82.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
39.0%	2	`x`
37.4%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
8.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
8.0%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Memory

-28.7MiB live, 8.3MiB 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:

5.0ms	(-.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
5.7%	1	`x`
5.7%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch26.0ms (0.3%)

Memory

7.6MiB live, 43.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
24.0ms	4.670762972002682e+151	4.979645718103361e+154

Samples

15.0ms

128×

valid

Compiler

Compiled 166 to 148 computations (10.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sqrt: 4.0ms (35.2% of total)

ival-div: 3.0ms (26.4% of total)

adjust: 2.0ms (17.6% of total)

ival-add: 1.0ms (8.8% of total)

ival-sub: 1.0ms (8.8% of total)

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

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

exact: 0.0ms (0% of total)

simplify28.0ms (0.3%)

Memory

27.9MiB live, 65.1MiB allocated

Algorithm

1×	egg-herbie

Rules

26×	`+-commutative-binary64-+.f64`
24×	`-commutative-binary64-.f64`
24×	`sub-neg-binary64-neg.f64-+.f64--.f64`
22×	`neg-sub0-binary64--.f64-neg.f64`
22×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	379
1	130	379
2	154	378
3	176	378
4	184	378
5	186	378

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (+ (* (sqrt (+ 1 x)) (neg (sqrt (+ 1 x)))) (* (sqrt x) (neg (sqrt (+ 1 x))))) (fma.f64 #s(literal -2 binary64) x #s(literal -3/2 binary64))))
(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* (sqrt (/ 1 x)) 1/2)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(if (<=.f64 x #s(literal 4600000000000000259272652606512016799213132235005633869259928535246893330689236690036551753838824648947751718403393963071093676518791710391413096650375168 binary64)) (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))))
(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Outputs
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (* (- (+ x 1) x) (/ -1 (sqrt x))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (+ (* (sqrt (+ 1 x)) (neg (sqrt (+ 1 x)))) (* (sqrt x) (neg (sqrt (+ 1 x))))) (fma.f64 #s(literal -2 binary64) x #s(literal -3/2 binary64))))
(/.f64 #s(approx (/ (* (- (+ x 1) x) (/ -1 (sqrt x))) (+ (sqrt (+ 1 x)) (sqrt x))) (/.f64 #s(literal -1/2 binary64) x)) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* (sqrt (/ 1 x)) 1/2)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (* x x)) (/.f64 #s(approx (+ (* (/ (sqrt (/ 1 x)) x) 5/8) (* (sqrt (/ 1 x)) 1/2)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (+ (* -1/2 (+ (* (sqrt (/ 1 (pow x 5))) (+ (* 1/2 x) 1)) (neg (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (pow x 3)))) (sqrt x))))) (* -1/2 (sqrt (/ 1 x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
(if (<=.f64 x #s(literal 4600000000000000259272652606512016799213132235005633869259928535246893330689236690036551753838824648947751718403393963071093676518791710391413096650375168 binary64)) (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))) (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))))
(if (<=.f64 x #s(literal 4600000000000000259272652606512016799213132235005633869259928535246893330689236690036551753838824648947751718403393963071093676518791710391413096650375168 binary64)) (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x))))
(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (* (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))) (+ (sqrt x) (sqrt (+ x 1)))) (+.f64 (sqrt.f64 x) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

soundness1.6s (19.5%)

Memory

-156.1MiB live, 1 086.3MiB allocated

Rules

16 898×	`lower-fma.f64`
16 898×	`lower-fma.f32`
11 004×	`lower-fma.f64`
11 004×	`lower-fma.f32`
10 756×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	155	744
1	437	667
2	1370	639
3	4606	634
0	8302	583
0	51	321
0	80	299
1	353	273
2	2802	267
0	8206	255
0	73	377
0	106	360
1	411	320
2	3375	320
0	8514	314
0	8	27
0	14	27
1	66	23
2	565	23
3	6719	23
0	8113	23
0	567	4875
1	1751	4093
2	5957	4049
0	8359	3836
0	646	4800
1	2003	4039
2	6931	4035
0	8089	3822
0	695	4654
1	2106	3895
2	7348	3856
0	8036	3686

Stop Event

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

Compiler

Compiled 602 to 310 computations (48.5% saved)

preprocess121.0ms (1.4%)

Memory: 41.2MiB live, 156.3MiB allocated
Compiler: Compiled 262 to 130 computations (50.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze2.0ms (0%)

sample2.3s (27.1%)

explain211.0ms (2.5%)

preprocess22.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize68.0ms (0.8%)

series7.0ms (0.1%)

simplify176.0ms (2.1%)

rewrite199.0ms (2.4%)

eval72.0ms (0.9%)

prune68.0ms (0.8%)

simplify265.0ms (3.2%)

localize288.0ms (3.4%)

series34.0ms (0.4%)

simplify220.0ms (2.6%)

rewrite161.0ms (1.9%)

eval285.0ms (3.4%)

prune58.0ms (0.7%)

simplify124.0ms (1.5%)

localize245.0ms (2.9%)

series25.0ms (0.3%)

simplify156.0ms (1.9%)

rewrite169.0ms (2%)

eval260.0ms (3.1%)

prune48.0ms (0.6%)

simplify187.0ms (2.2%)

localize252.0ms (3%)

series23.0ms (0.3%)

simplify169.0ms (2%)

rewrite151.0ms (1.8%)

eval173.0ms (2.1%)

prune53.0ms (0.6%)

regimes39.0ms (0.5%)

regimes15.0ms (0.2%)

regimes15.0ms (0.2%)

regimes6.0ms (0.1%)

regimes12.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes6.0ms (0.1%)

bsearch26.0ms (0.3%)

simplify28.0ms (0.3%)

soundness1.6s (19.5%)

preprocess121.0ms (1.4%)

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