Metrics for Main:bigenough3 from C

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze6.0ms (0.1%)

Memory

-42.8MiB live, 4.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
80%	50%	12.5%	0%	0%	37.5%	0%	4
88.9%	50%	6.2%	0%	0%	43.7%	0%	5
94.1%	50%	3.1%	0%	0%	46.9%	0%	6
97%	50%	1.6%	0%	0%	48.4%	0%	7
98.5%	50%	0.8%	0%	0%	49.2%	0%	8
99.2%	50%	0.4%	0%	0%	49.6%	0%	9
99.6%	50%	0.2%	0%	0%	49.8%	0%	10
99.8%	50%	0.1%	0%	0%	49.9%	0%	11
99.9%	50%	0%	0%	0%	49.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.4s (18.3%)

Memory

46.1MiB live, 1 103.3MiB allocated

Samples

420.0ms	4 003×	1	valid
395.0ms	4 253×	0	valid
1.0ms	14×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 626.0ms

ival-sub: 202.0ms (32.3% of total)

ival-sqrt: 173.0ms (27.7% of total)

ival-add: 139.0ms (22.2% of total)

adjust: 98.0ms (15.7% of total)

ival-true: 6.0ms (1% of total)

exact: 5.0ms (0.8% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain200.0ms (2.5%)

Memory

-8.0MiB live, 91.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
129	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
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 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	129	0

Confusion

	Predicted +	Predicted -
+	129	0
-	0	127

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	127
1	129

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms	258×	1	valid
12.0ms	254×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-sqrt: 11.0ms (46.1% of total)

adjust: 4.0ms (16.8% of total)

ival-add: 4.0ms (16.8% of total)

ival-sub: 3.0ms (12.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess42.0ms (0.5%)

Memory

-25.1MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize60.0ms (0.8%)

Memory

-4.3MiB live, 34.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.0078125	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	30.962048353886708	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

40.0ms	127×	0	valid
13.0ms	129×	1	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-sqrt: 39.0ms (85.7% of total)

adjust: 2.0ms (4.4% of total)

ival-add: 2.0ms (4.4% of total)

ival-sub: 2.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

simplify206.0ms (2.6%)

Memory

20.4MiB live, 172.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	498
1	299	446
2	804	442
3	2258	434
4	4617	434
0	8205	398

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

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

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

rewrite291.0ms (3.7%)

Memory

-24.4MiB live, 216.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16

Stop Event

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

Counts

4 → 357

Calls

Call 1

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

Outputs
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eval69.0ms (0.9%)

Memory: 22.0MiB live, 140.6MiB allocated
Compiler: Compiled 7 571 to 1 407 computations (81.4% saved)

prune21.0ms (0.3%)

Memory

-1.9MiB live, 36.6MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	394	9	403
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	395	9	404

Accuracy

100.0%

Counts

404 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	3.5%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
▶	49.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	51.9%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
▶	51.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	50.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	51.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	50.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶	53.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 206 to 150 computations (27.2% saved)

simplify294.0ms (3.7%)

Memory

-17.1MiB live, 140.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	184
0	44	184
1	64	184
2	93	184
3	238	184
4	606	184
5	1524	184
6	3101	184
7	4125	184
8	4465	184
9	4709	184
10	4767	184
11	4837	184
12	5438	184
13	6239	184
14	6404	184
15	6466	184
16	6480	184
17	6481	184
18	6481	184
19	6494	184
20	6574	184
21	7082	184
0	7082	184

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize86.0ms (1.1%)

Memory

1.6MiB live, 200.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0.14453125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.23828125	(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy	31.455065906212184	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.0390625	(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy	0	(sqrt.f64 x)
accuracy	29.5926544551845	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy	30.962048353886708	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	30.70877200462445	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy	30.962048353886708	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
accuracy	0.14453125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	29.584277314612937	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Samples

43.0ms	129×	1	valid
23.0ms	127×	0	valid

Compiler

Compiled 150 to 25 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 12.0ms (26.8% of total)

ival-add: 9.0ms (20.1% of total)

ival-sqrt: 8.0ms (17.9% of total)

adjust: 6.0ms (13.4% of total)

ival-div: 5.0ms (11.2% of total)

ival-sub: 4.0ms (8.9% of total)

exact: 1.0ms (2.2% of total)

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

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

series16.0ms (0.2%)

Memory

5.7MiB live, 44.6MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) x) (patch (/.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) (patch (-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (patch #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) (patch (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (patch (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (patch (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #<representation binary64>) () ())

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (- 1 (sqrt x)))
2.0ms	x	@	0	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (- 1 (sqrt x)))
2.0ms	x	@	inf	((- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (sqrt (/ 1 x)) (/ 1 x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (- (sqrt (+ x 1)) (sqrt x)) (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (- 1 (sqrt x)))

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify174.0ms (2.2%)

Memory

8.4MiB live, 324.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	2572
1	506	2290
2	1543	2258
3	4520	2225
0	8377	2052

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

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

rewrite199.0ms (2.5%)

Memory

17.4MiB live, 329.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	152
0	44	152
1	187	144
2	1419	144
0	8473	141

Stop Event

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

Counts

17 → 500

Calls

Call 1

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

Outputs
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eval158.0ms (2%)

Memory: 13.1MiB live, 251.4MiB allocated
Compiler: Compiled 19 303 to 2 360 computations (87.8% saved)

prune34.0ms (0.4%)

Memory

-6.1MiB live, 65.9MiB allocated

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	878	6	884
Fresh	3	1	4
Picked	2	3	5
Done	0	0	0
Total	883	10	893

Accuracy

100.0%

Counts

893 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	49.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	51.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	50.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	51.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	53.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
	50.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
▶	2.9%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x))))

Compiler

Compiled 168 to 137 computations (18.5% saved)

simplify405.0ms (5.1%)

Memory

6.3MiB live, 85.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	284
0	58	284
1	87	284
2	141	284
3	382	284
4	859	284
5	2027	284
6	4099	284
7	5289	284
8	5651	284
9	5910	284
10	5956	284
11	5993	284
12	6002	284
13	6045	284
14	6061	284
15	6061	284
16	6237	284
17	6265	284
18	6306	284
19	6344	284
20	6367	284
21	6375	284
22	6377	284
0	6377	274

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize124.0ms (1.6%)

Memory

6.7MiB live, 125.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.0390625	(fma.f64 (fma.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy	32.52934644997478	#s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.2890625	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy	29.584277314612937	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.0390625	(fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
accuracy	31.57000162360534	#s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.05078125	(.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x))
accuracy	30.891171394322935	#s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x)))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x))))
accuracy	0	(sqrt.f64 x)
accuracy	0.23828125	(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy	31.267389560616166	#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	31.455065906212184	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))

Samples

51.0ms	129×	1	valid
27.0ms	127×	0	valid

Compiler

Compiled 187 to 27 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 19.0ms (32.7% of total)

ival-add: 15.0ms (25.8% of total)

ival-div: 7.0ms (12.1% of total)

ival-sqrt: 7.0ms (12.1% of total)

adjust: 6.0ms (10.3% of total)

ival-sub: 4.0ms (6.9% of total)

exact: 1.0ms (1.7% of total)

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

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

series23.0ms (0.3%)

Memory

-14.3MiB live, 21.9MiB allocated

Counts

20 → 240

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

10.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify192.0ms (2.4%)

Memory

27.9MiB live, 259.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	152	2738
1	407	2516
2	1162	2460
3	3388	2407
0	8183	2223

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

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

rewrite193.0ms (2.4%)

Memory

-31.9MiB live, 221.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	260
0	58	260
1	227	254
2	1662	254
0	8273	244

Stop Event

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

Counts

20 → 333

Calls

Call 1

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

Outputs
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eval88.0ms (1.1%)

Memory: 30.9MiB live, 146.1MiB allocated
Compiler: Compiled 14 493 to 1 737 computations (88% saved)

prune28.0ms (0.4%)

Memory

-14.3MiB live, 60.6MiB allocated

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	693	3	696
Fresh	0	2	2
Picked	0	5	5
Done	0	3	3
Total	693	13	706

Accuracy

100.0%

Counts

706 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	49.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	51.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	50.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	51.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	3.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
✓	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	53.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
▶	50.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
✓	2.9%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x))))
▶	3.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))))
▶	1.9%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))))

Compiler

Compiled 178 to 145 computations (18.5% saved)

simplify256.0ms (3.2%)

Memory

8.2MiB live, 126.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
cost-diff	128	(neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
cost-diff	320	(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
cost-diff	0	#s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
cost-diff	0	#s(approx (+ (* 1/16 x) -1/8) (*.f64 #s(literal 1/16 binary64) x))
cost-diff	0	(.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x)))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))))
cost-diff	0	#s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64))
cost-diff	0	(.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x)))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))))
cost-diff	0	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	361
0	64	365
1	108	351
2	200	347
3	501	347
4	1172	347
5	2578	347
6	4983	347
7	6040	347
8	6508	347
9	6593	347
10	6636	347
11	6642	347
12	6642	347
13	6644	347
14	7087	347
0	8244	320

Stop Event

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

Calls

Call 1

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

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

localize147.0ms (1.9%)

Memory

-0.7MiB live, 193.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	0.27181625976844204	(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))
accuracy	0.2890625	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	31.455065906212184	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
accuracy	0.0390625	(fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x))))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
accuracy	31.57000162360534	#s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64))
accuracy	31.63373372015522	#s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))
accuracy	0.05078125	(.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))
accuracy	30.891171394322935	#s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x)))
accuracy	31.049832984474953	#s(approx (+ (* 1/16 x) -1/8) (*.f64 #s(literal 1/16 binary64) x))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))))
accuracy	0.05078125	(.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))
accuracy	30.891171394322935	#s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x)))
accuracy	31.265909694787407	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))))
accuracy	32.52934644997478	#s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64))
accuracy	0.0078125	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.015625	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.1640625	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	31.00710771487272	(-.f64 (+.f64 #s(literal 1 binary64) x) x)

Samples

62.0ms	129×	1	valid
52.0ms	127×	0	valid

Compiler

Compiled 221 to 33 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-mult: 37.0ms (40.5% of total)

adjust: 14.0ms (15.3% of total)

ival-add: 12.0ms (13.1% of total)

ival-div: 9.0ms (9.8% of total)

ival-sqrt: 8.0ms (8.8% of total)

ival-sub: 6.0ms (6.6% of total)

ival-neg: 3.0ms (3.3% of total)

exact: 1.0ms (1.1% of total)

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

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

series27.0ms (0.3%)

Memory

-1.5MiB live, 35.9MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify319.0ms (4%)

Memory

15.2MiB live, 172.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	287	3333
1	844	3092
2	2621	3055
3	6883	3051
0	8311	2825

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

Calls

Call 1

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

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

rewrite576.0ms (7.3%)

Memory

-59.9MiB live, 269.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	328
0	64	328
1	261	316
2	2025	316
0	9589	287

Stop Event

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

Counts

22 → 495

Calls

Call 1

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

Outputs
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eval308.0ms (3.9%)

Memory: -15.1MiB live, 244.8MiB allocated
Compiler: Compiled 18 591 to 2 394 computations (87.1% saved)

prune31.0ms (0.4%)

Memory

5.4MiB live, 81.1MiB allocated

Pruning

13 alts after pruning (3 fresh and 10 done)

	Pruned	Kept	Total
New	840	3	843
Fresh	0	0	0
Picked	3	2	5
Done	0	8	8
Total	843	13	856

Accuracy

100.0%

Counts

856 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	49.4%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	51.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	50.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	51.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	3.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(approx (+ (* (+ (* 1/16 x) -1/8) x) 1/2) #s(literal 1/2 binary64)) x #s(approx (- 1 (sqrt x)) (neg.f64 (sqrt.f64 x)))))
✓	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓	53.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
	50.6%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) x)))
✓	53.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	2.9%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x))))
	1.9%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)) x) x)))
✓	3.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) (.f64 #s(literal 1/16 binary64) x)) (.f64 x x))))

Compiler

Compiled 346 to 193 computations (44.2% saved)

regimes13.0ms (0.2%)

Memory

30.0MiB live, 30.0MiB allocated

Counts

22 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes32.0ms (0.4%)

Memory

-22.3MiB live, 15.2MiB allocated

Counts

16 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

25.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
5.0ms	x

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes10.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

15 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.9%	2	`x`
99.9%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

12 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	2	`x`
99.5%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes46.0ms (0.6%)

Memory

-40.2MiB live, 8.0MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

42.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
51.5%	1	`x`
51.5%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
49.4%	1	`x`
49.4%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
1.9%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
1.9%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.774199962615967e-8	0.9967082365477302

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.774199962615967e-8	0.9967082365477302

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.774199962615967e-8	0.9967082365477302

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.774199962615967e-8	0.9967082365477302

Compiler

Compiled 10 to 10 computations (0% saved)

simplify35.0ms (0.4%)

Memory

-17.4MiB live, 55.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	239
1	68	239
2	74	239
3	76	239
4	77	239

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))))

Outputs
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) #s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 #s(approx (+ ( 1/16 x) -1/8) #s(literal -1/8 binary64)) (*.f64 x x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (+ (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (- 1 (sqrt x))) (.f64 (.f64 x x) #s(approx (+ (* 1/16 x) -1/8) #s(literal -1/8 binary64)))))

soundness1.6s (20.1%)

Memory

5.6MiB live, 856.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	2572
1	506	2290
2	1543	2258
3	4520	2225
0	8377	2052
0	287	3333
1	844	3092
2	2621	3055
3	6883	3051
0	8311	2825
0	27	152
0	44	152
1	187	144
2	1419	144
0	8473	141
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	113	498
1	299	446
2	804	442
3	2258	434
4	4617	434
0	8205	398
0	152	2738
1	407	2516
2	1162	2460
3	3388	2407
0	8183	2223

Stop Event

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

Compiler

Compiled 290 to 158 computations (45.5% saved)

preprocess128.0ms (1.6%)

Memory: 6.9MiB live, 180.6MiB allocated
Compiler: Compiled 310 to 108 computations (65.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

start0.0ms (0%)

analyze6.0ms (0.1%)

sample1.4s (18.3%)

explain200.0ms (2.5%)

preprocess42.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize60.0ms (0.8%)

series5.0ms (0.1%)

simplify206.0ms (2.6%)

rewrite291.0ms (3.7%)

eval69.0ms (0.9%)

prune21.0ms (0.3%)

simplify294.0ms (3.7%)

localize86.0ms (1.1%)

series16.0ms (0.2%)

simplify174.0ms (2.2%)

rewrite199.0ms (2.5%)

eval158.0ms (2%)

prune34.0ms (0.4%)

simplify405.0ms (5.1%)

localize124.0ms (1.6%)

series23.0ms (0.3%)

simplify192.0ms (2.4%)

rewrite193.0ms (2.4%)

eval88.0ms (1.1%)

prune28.0ms (0.4%)

simplify256.0ms (3.2%)

localize147.0ms (1.9%)

series27.0ms (0.3%)

simplify319.0ms (4%)

rewrite576.0ms (7.3%)

eval308.0ms (3.9%)

prune31.0ms (0.4%)

regimes13.0ms (0.2%)

regimes32.0ms (0.4%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes46.0ms (0.6%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify35.0ms (0.4%)

soundness1.6s (20.1%)

preprocess128.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18