Metrics for 2isqrt (example 3.6)

analyze2.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.1s (19.8%)

Memory

43.0MiB live, 1 796.2MiB allocated

Samples

1.4s	6 884×	1	valid
303.0ms	1 114×	2	valid
18.0ms	258×	0	valid

Precisions

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

ival-sqrt: 412.0ms (29.8% of total)

ival-div: 283.0ms (20.5% of total)

const: 189.0ms (13.7% of total)

adjust: 165.0ms (11.9% of total)

ival-add: 126.0ms (9.1% of total)

ival-sub: 102.0ms (7.4% of total)

ival-<: 48.0ms (3.5% of total)

ival->: 38.0ms (2.7% of total)

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

exact: 7.0ms (0.5% of total)

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

Bogosity

preprocess27.0ms (0.2%)

Memory

-3.7MiB live, 34.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

explain150.0ms (1.4%)

Memory

-21.8MiB live, 215.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`	cancellation	173	0

Confusion

	Predicted +	Predicted -
+	173	0
-	0	83

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	173	0	0
-	0	0	83

Precision?

1.0

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

74.0ms	442×	1	valid
14.0ms	62×	2	valid
0.0ms	8×	0	valid

Compiler

Compiled 92 to 36 computations (60.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-add: 21.0ms (30.7% of total)

ival-sqrt: 16.0ms (23.4% of total)

ival-div: 14.0ms (20.5% of total)

adjust: 9.0ms (13.2% of total)

ival-sub: 8.0ms (11.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify17.0ms (0.2%)

Memory

-22.6MiB live, 15.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize47.0ms (0.4%)

Memory

28.7MiB live, 67.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	39.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

29.0ms	221×	1	valid
6.0ms	31×	2	valid
0.0ms	4×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-div: 8.0ms (32.4% of total)

ival-sqrt: 7.0ms (28.4% of total)

adjust: 5.0ms (20.3% of total)

ival-add: 2.0ms (8.1% of total)

ival-sub: 2.0ms (8.1% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

simplify464.0ms (4.3%)

Memory

-6.9MiB live, 745.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite253.0ms (2.3%)

Memory

4.6MiB live, 360.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

4 → 238

Calls

Call 1

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

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

eval34.0ms (0.3%)

Memory: 2.8MiB live, 82.8MiB allocated
Compiler: Compiled 7 402 to 705 computations (90.5% saved)

prune50.0ms (0.5%)

Memory

-22.8MiB live, 135.9MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	276	10	286
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	276	11	287

Accuracy

84.5%

Counts

287 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	40.9%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
✓	39.2%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	26.9%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	28.6%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	5.5%	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x)))
	5.5%	(.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
▶	84.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
▶	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
	69.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
▶	5.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 372 to 212 computations (43% saved)

simplify309.0ms (2.9%)

Memory

28.4MiB live, 489.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
✓	cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	1088	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	cost-diff	0	#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))

Rules

11 290×	`lower-fma.f32`
11 284×	`lower-fma.f64`
3 122×	`lower-*.f32`
3 114×	`lower-*.f64`
1 882×	`lower-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	374
0	69	354
1	124	342
2	254	338
3	539	338
4	1279	338
5	3120	338
6	6699	338
0	8214	338

Stop Event

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

Calls

Call 1

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

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

localize207.0ms (1.9%)

Memory

22.4MiB live, 414.4MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	accuracy	98.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))
✓	accuracy	52.7%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	6.5%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.9%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	98.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	accuracy	85.5%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	98.8%	#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	39.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	5.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	84.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
✓	accuracy	71.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

114.0ms	221×	1	valid
22.0ms	31×	2	valid
1.0ms	4×	0	valid

Compiler

Compiled 335 to 38 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-div: 20.0ms (20.6% of total)

ival-sqrt: 18.0ms (18.5% of total)

adjust: 17.0ms (17.5% of total)

ival-sub: 14.0ms (14.4% of total)

ival-mult: 14.0ms (14.4% of total)

ival-add: 12.0ms (12.4% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.3%)

Memory

17.0MiB live, 54.7MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))))
1.0ms	x	@	-inf	(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
1.0ms	x	@	0	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
1.0ms	x	@	0	(/ 1 (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))))
1.0ms	x	@	inf	(/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))))

simplify434.0ms (4%)

Memory

-23.0MiB live, 602.0MiB allocated

Algorithm

1×	egg-herbie

Rules

17 302×	`lower-fma.f64`
17 302×	`lower-fma.f32`
5 380×	`lower-*.f64`
5 380×	`lower-*.f32`
5 092×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	434	3992
1	1329	3402
2	4743	3349
0	8775	3156

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 263

Calls

Call 1

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

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

rewrite394.0ms (3.6%)

Memory

-25.7MiB live, 487.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 458×	`lower-*.f32`
5 450×	`lower-*.f64`
3 512×	`lower-/.f32`
3 496×	`lower-/.f64`
2 886×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	279
0	69	267
1	314	217
2	2742	212
0	8848	209

Stop Event

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

Counts

22 → 625

Calls

Call 1

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

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

eval192.0ms (1.8%)

Memory: 33.8MiB live, 270.4MiB allocated
Compiler: Compiled 29 583 to 3 145 computations (89.4% saved)

prune207.0ms (1.9%)

Memory

-21.8MiB live, 452.1MiB allocated

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	1 227	16	1 243
Fresh	3	2	5
Picked	4	1	5
Done	1	0	1
Total	1 235	19	1 254

Accuracy

100.0%

Counts

1 254 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	84.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	84.3%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	45.1%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (fma.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))))
▶	69.2%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))))
▶	5.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
	5.5%	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x x)))
	5.5%	(.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
	69.3%	#s(approx (/ 1 (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64))))
▶	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) x)) x))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (.f64 x (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
▶	84.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x)))
	84.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (fma.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x)))) (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (sqrt.f64 x) (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) (.f64 x x)))
	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
▶	98.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
	83.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	5.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	98.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)))

Compiler

Compiled 664 to 364 computations (45.2% saved)

simplify278.0ms (2.6%)

Memory

-0.5MiB live, 450.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	cost-diff	384	(/.f64 (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x))
✓	cost-diff	960	(.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
✓	cost-diff	384	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)
✓	cost-diff	512	(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x x)))
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))
✓	cost-diff	0	#s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	#s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x))
✓	cost-diff	128	(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64))
✓	cost-diff	384	(/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x)
✓	cost-diff	384	(/.f64 (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x)

Rules

9 630×	`lower-fma.f32`
9 628×	`lower-fma.f64`
2 998×	`lower-*.f32`
2 984×	`lower-*.f64`
1 642×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	388
0	74	378
1	124	362
2	209	354
3	377	354
4	662	335
5	1653	335
6	3998	335
7	7958	335
0	8255	330

Stop Event

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

Calls

Call 1

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

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

localize326.0ms (3%)

Memory

-9.9MiB live, 433.0MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	accuracy	99.2%	(/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))
✓	accuracy	84.4%	(/.f64 (.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) #s(literal 1/2 binary64)) (*.f64 x x))
✓	accuracy	66.5%	(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x)
✓	accuracy	99.6%	(*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	99.2%	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	98.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	98.8%	#s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
✓	accuracy	98.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))))
✓	accuracy	71.3%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	98.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
✓	accuracy	5.6%	#s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x)
✓	accuracy	99.6%	(/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x)
✓	accuracy	99.2%	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	98.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) #s(literal -1/2 binary64)) x) x))

Samples

184.0ms	221×	1	valid
63.0ms	31×	2	valid
1.0ms	4×	0	valid

Compiler

Compiled 322 to 45 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-div: 75.0ms (35.4% of total)

ival-mult: 58.0ms (27.4% of total)

ival-sqrt: 42.0ms (19.8% of total)

adjust: 18.0ms (8.5% of total)

ival-add: 11.0ms (5.2% of total)

ival-sub: 5.0ms (2.4% of total)

exact: 1.0ms (0.5% of total)

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

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

series27.0ms (0.2%)

Memory

1.8MiB live, 43.2MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2)
1.0ms	x	@	inf	(/ (+ (* x 1/4) 1) (* x (sqrt x)))
1.0ms	x	@	-inf	(/ (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) x)
1.0ms	x	@	0	(/ (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) x)
0.0ms	x	@	-inf	(* 2 (sqrt (* x (* x x))))

simplify471.0ms (4.4%)

Memory

20.4MiB live, 813.8MiB allocated

Algorithm

1×	egg-herbie

Rules

18 410×	`lower-fma.f64`
18 410×	`lower-fma.f32`
5 930×	`lower-+.f64`
5 930×	`lower-+.f32`
4 644×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	341	4281
1	1045	3836
2	3621	3641
0	8271	3462

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

rewrite376.0ms (3.5%)

Memory

20.0MiB live, 610.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 056×	`lower-/.f32`
5 036×	`lower-/.f64`
4 208×	`lower-fma.f32`
4 206×	`lower-fma.f64`
3 354×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	334
0	74	324
1	325	279
2	2977	271
0	9408	259

Stop Event

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

Counts

22 → 815

Calls

Call 1

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

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

eval430.0ms (4%)

Memory: 4.7MiB live, 265.2MiB allocated
Compiler: Compiled 27 706 to 3 152 computations (88.6% saved)

prune248.0ms (2.3%)

Memory

-20.2MiB live, 281.7MiB allocated

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	1 275	10	1 285
Fresh	7	6	13
Picked	4	1	5
Done	0	1	1
Total	1 286	18	1 304

Accuracy

100.0%

Counts

1 304 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	84.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	84.3%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))
✓	5.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
	5.5%	(.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
	69.3%	#s(approx (/ 1 (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	97.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x (sqrt.f64 x))) (.f64 x #s(literal -2 binary64))))
▶	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64))))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 x)) x))
	98.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (/.f64 x (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (sqrt.f64 x))))
	76.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (.f64 x (*.f64 x (sqrt.f64 x)))))
▶	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
▶	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (/.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))) x)))
	98.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (*.f64 (/.f64 #s(approx (/ (- 1 x) (sqrt x)) (neg.f64 (sqrt.f64 x))) x) (/.f64 #s(literal -1/2 binary64) x)))
	83.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
✓	5.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	99.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)))

Compiler

Compiled 474 to 294 computations (38% saved)

simplify364.0ms (3.4%)

Memory

15.4MiB live, 365.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (fma.f64 x x x))
✓	cost-diff	0	(+.f64 x (sqrt.f64 (fma.f64 x x x)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
✓	cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64))))
✓	cost-diff	512	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64)))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	#s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
✓	cost-diff	0	#s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))
✓	cost-diff	0	(.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	cost-diff	0	(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
✓	cost-diff	0	#s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x))
✓	cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)))
✓	cost-diff	320	(.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x))))

Rules

10 752×	`lower-fma.f32`
10 750×	`lower-fma.f64`
3 450×	`lower-*.f32`
3 438×	`lower-*.f64`
1 572×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	446
0	85	446
1	142	446
2	263	446
3	531	438
4	1049	422
5	2739	422
6	4932	422
0	8075	416

Stop Event

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

Calls

Call 1

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

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

localize336.0ms (3.1%)

Memory

-6.3MiB live, 392.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	52.7%	(sqrt.f64 (fma.f64 x x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.2%	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	98.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64))))
✓	accuracy	84.4%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) #s(literal -2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
✓	accuracy	98.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
✓	accuracy	98.8%	#s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
✓	accuracy	98.8%	#s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))
✓	accuracy	84.4%	(/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)))
✓	accuracy	99.7%	(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x)
✓	accuracy	99.7%	#s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))) x))

Samples

178.0ms	221×	1	valid
27.0ms	31×	2	valid
1.0ms	4×	0	valid

Compiler

Compiled 316 to 48 computations (84.8% saved)

Precisions

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

ival-div: 63.0ms (47.6% of total)

adjust: 19.0ms (14.4% of total)

ival-sqrt: 17.0ms (12.9% of total)

ival-mult: 17.0ms (12.9% of total)

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

ival-sub: 4.0ms (3% of total)

exact: 1.0ms (0.8% of total)

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

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

series19.0ms (0.2%)

Memory

11.2MiB live, 49.2MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

69 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* -1/2 (* (sqrt (/ 1 x)) (- -1 (/ -3/4 x))))
1.0ms	x	@	0	(* -1/2 (* (sqrt (/ 1 x)) (- -1 (/ -3/4 x))))
0.0ms	x	@	inf	(* -1/2 (* (sqrt (/ 1 x)) (- -1 (/ -3/4 x))))
0.0ms	x	@	-inf	(/ (* -1/2 (* (sqrt (/ 1 x)) (- -1 (/ -3/4 x)))) x)
0.0ms	x	@	-inf	(* 1/2 (sqrt (/ 1 x)))

simplify424.0ms (3.9%)

Memory

6.8MiB live, 802.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16 358×	`lower-fma.f64`
16 358×	`lower-fma.f32`
5 088×	`lower-*.f64`
5 088×	`lower-*.f32`
4 504×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	415	4140
1	1278	3738
2	4170	3510
0	8396	3341

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 275

Calls

Call 1

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

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

rewrite319.0ms (2.9%)

Memory

-15.3MiB live, 661.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 104×	`lower-/.f32`
5 086×	`lower-/.f64`
3 788×	`lower-fma.f32`
3 786×	`lower-fma.f64`
3 404×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	383
0	85	383
1	351	348
2	2967	339
0	9412	323

Stop Event

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

Counts

23 → 562

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x)))
(+.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (*.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x)))
(/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 27/64 binary64) (.f64 x (*.f64 x x))))) (fma.f64 (/.f64 #s(literal -3/4 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 9/16 binary64) (.f64 x x)))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 27/64 binary64) (.f64 x (*.f64 x x)))))) (neg.f64 (fma.f64 (/.f64 #s(literal -3/4 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 9/16 binary64) (.f64 x x))))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/4 binary64) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x)) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (-.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x)) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x))) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 3/4 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (-.f64 (.f64 (.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 (/.f64 #s(literal 3/4 binary64) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))))
(*.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)))
(.f64 (.f64 #s(literal -1/2 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))))))
#s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x))))))
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(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log1p.f64 x)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x x))))

eval137.0ms (1.3%)

Memory: -14.0MiB live, 234.7MiB allocated
Compiler: Compiled 17 090 to 2 209 computations (87.1% saved)

prune116.0ms (1.1%)

Memory

11.8MiB live, 332.3MiB allocated

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	905	8	913
Fresh	8	3	11
Picked	3	2	5
Done	0	2	2
Total	916	15	931

Accuracy

100.0%

Counts

931 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	84.3%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	99.4%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	99.7%	(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.6%	(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	84.3%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))
✓	5.6%	(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
	69.3%	#s(approx (/ (/ 1 (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)))
✓	83.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
	97.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (/.f64 (sqrt.f64 x) (-.f64 #s(literal 1 binary64) x))) x)))
	83.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))))
✓	5.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	99.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (/.f64 (*.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) x)))
	98.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) 1/2) (* x x)) (.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 3/4 binary64) x)) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal -1/2 binary64))))

Compiler

Compiled 860 to 285 computations (66.9% saved)

regimes24.0ms (0.2%)

Memory

7.3MiB live, 46.2MiB allocated

Counts

45 → 1

Calls

Call 1

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

Outputs

(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (*.f64 x (*.f64 x x))))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))

Calls

2 calls:

13.0ms	x
9.0ms	(-.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 14 to 9 computations (35.7% saved)

regimes22.0ms (0.2%)

Memory

-0.5MiB live, 38.5MiB allocated

Counts

41 → 1

Calls

Call 1

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

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

Calls

2 calls:

11.0ms	x
8.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	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 14 to 9 computations (35.7% saved)

regimes10.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes8.0ms (0.1%)

Memory

-28.6MiB live, 9.8MiB 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)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (- (sqrt (/ 1 x)) (sqrt x)) (neg.f64 (sqrt.f64 x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))

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

Calls

2 calls:

5.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0%)

Memory

8.4MiB live, 8.4MiB 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)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) #s(literal 1/2 binary64)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))

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

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
97.4%	1	`x`
97.4%	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 14 to 9 computations (35.7% saved)

regimes4.0ms (0%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

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
83.2%	1	`x`
83.2%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes4.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
83.1%	1	`x`
83.1%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes3.0ms (0%)

Memory

5.7MiB live, 5.7MiB 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)))

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
5.6%	1	`x`
5.6%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify16.0ms (0.1%)

Memory

-45.7MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	227
1	100	227

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Outputs
(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(approx (/ 1 (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (/ (* (/ (- 1 x) (sqrt x)) -1/2) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ 1 x)) (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x))))) (.f64 (.f64 x (sqrt.f64 x)) #s(literal 2 binary64))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(approx (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

soundness1.7s (16%)

Memory

45.3MiB live, 1 344.1MiB allocated

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
18 410×	`lower-fma.f64`
18 410×	`lower-fma.f32`
17 302×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	341	4281
1	1045	3836
2	3621	3641
0	8271	3462
0	50	334
0	74	324
1	325	279
2	2977	271
0	9408	259
0	415	4140
1	1278	3738
2	4170	3510
0	8396	3341
0	41	279
0	69	267
1	314	217
2	2742	212
0	8848	209
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416
0	434	3992
1	1329	3402
2	4743	3349
0	8775	3156
0	59	383
0	85	383
1	351	348
2	2967	339
0	9412	323

Stop Event

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

Compiler

Compiled 328 to 165 computations (49.7% saved)

preprocess169.0ms (1.6%)

Memory: 1.4MiB live, 114.4MiB allocated
Compiler: Compiled 256 to 122 computations (52.3% 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

analyze2.0ms (0%)

sample2.1s (19.8%)

preprocess27.0ms (0.2%)

explain150.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify17.0ms (0.2%)

localize47.0ms (0.4%)

series6.0ms (0.1%)

simplify464.0ms (4.3%)

rewrite253.0ms (2.3%)

eval34.0ms (0.3%)

prune50.0ms (0.5%)

simplify309.0ms (2.9%)

localize207.0ms (1.9%)

series28.0ms (0.3%)

simplify434.0ms (4%)

rewrite394.0ms (3.6%)

eval192.0ms (1.8%)

prune207.0ms (1.9%)

simplify278.0ms (2.6%)

localize326.0ms (3%)

series27.0ms (0.2%)

simplify471.0ms (4.4%)

rewrite376.0ms (3.5%)

eval430.0ms (4%)

prune248.0ms (2.3%)

simplify364.0ms (3.4%)

localize336.0ms (3.1%)

series19.0ms (0.2%)

simplify424.0ms (3.9%)

rewrite319.0ms (2.9%)

eval137.0ms (1.3%)

prune116.0ms (1.1%)

regimes24.0ms (0.2%)

regimes22.0ms (0.2%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

simplify16.0ms (0.1%)

soundness1.7s (16%)

preprocess169.0ms (1.6%)

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