Metrics for 2sqrt (example 3.1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.4s (18.3%)

Memory

54.4MiB live, 2 160.5MiB allocated

Samples

1.1s	7 977×	1	valid
30.0ms	279×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 861.0ms

ival-sqrt: 229.0ms (26.6% of total)

ival-add: 174.0ms (20.2% of total)

adjust: 162.0ms (18.8% of total)

const: 129.0ms (15% of total)

ival-sub: 87.0ms (10.1% of total)

ival->: 29.0ms (3.4% of total)

ival-<: 29.0ms (3.4% of total)

ival-and: 11.0ms (1.3% of total)

exact: 7.0ms (0.8% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain102.0ms (1.3%)

Memory

21.0MiB live, 179.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
256	-	2	(34.79802715775841)	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	0	-	`(+.f64 x #s(literal 1 binary64))`
0	-	0	-	`(sqrt.f64 x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	254	2

Confusion

	Predicted +	Predicted -
+	254	2
-	0	0

Precision

1.0

Recall

0.9921875

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	2	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

53.0ms	486×	1	valid
1.0ms	26×	0	valid

Compiler

Compiled 48 to 22 computations (54.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sqrt: 16.0ms (47.5% of total)

adjust: 8.0ms (23.7% of total)

ival-add: 5.0ms (14.8% of total)

ival-sub: 4.0ms (11.9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess20.0ms (0.3%)

Memory

-7.6MiB live, 30.7MiB allocated

Algorithm

1×	egg-herbie

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
46×	`sub-neg`

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 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify7.0ms (0.1%)

Memory

10.3MiB live, 10.3MiB 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))

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

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)

localize38.0ms (0.5%)

Memory

-26.3MiB live, 52.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	58.91860046783495	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

26.0ms	243×	1	valid
1.0ms	13×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sqrt: 10.0ms (54% of total)

adjust: 4.0ms (21.6% of total)

ival-add: 3.0ms (16.2% of total)

ival-sub: 2.0ms (10.8% 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

7.3MiB live, 7.3MiB 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))

simplify171.0ms (2.2%)

Memory

36.6MiB live, 183.5MiB allocated

Algorithm

1×	egg-herbie

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
3 884×	`lower-*.f64`
3 884×	`lower-*.f32`
2 664×	`lower--.f64`

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) (.f64 (.f64 x x) x))) #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) (.f64 (.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (.f64 x 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)))) 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) (.f64 (.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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)

rewrite183.0ms (2.3%)

Memory

-32.1MiB live, 245.6MiB allocated

Rules

5 090×	`lower-fma.f64`
5 090×	`lower-fma.f32`
3 260×	`lower-*.f64`
3 260×	`lower-*.f32`
2 676×	`lower-/.f64`

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
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))
(.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (-.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))
(*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 #s(literal 1 binary64) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))))
(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))
(.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))) (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))))
(.f64 (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))
(*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 (+.f64 #s(literal 1 binary64) x) x))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (fma.f64 (sqrt.f64 x) x (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (sqrt.f64 x) x) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (fma.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (fma.f64 (fma.f64 x x x) (sqrt.f64 (fma.f64 x x x)) (.f64 (*.f64 x x) x))))
(/.f64 (-.f64 (.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (+.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))) (.f64 (/.f64 (.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x)))) (/.f64 (*.f64 (sqrt.f64 x) x) (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))))
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (/.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))) (fma.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))))
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(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1 binary64)) (.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) #s(literal -1 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (.f64 x x) x #s(literal -1 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x) (fma.f64 (*.f64 x x) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64)) (.f64 (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal -1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64)) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 x) x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 x x) x #s(literal -1 binary64))) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 (sqrt.f64 x) x)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(fma.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(fabs.f64 (+.f64 #s(literal 1 binary64) x))
(hypot.f64 (neg.f64 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (fma.f64 x x x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 (fma.f64 x x x))))
(hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (fma.f64 x x x)))
(+.f64 (*.f64 x (/.f64 x (-.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x))))
(+.f64 #s(literal 1 binary64) x)
(+.f64 x #s(literal 1 binary64))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1 binary64)))
(exp.f64 (log1p.f64 x))
(.f64 (sqrt.f64 (.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 x))))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/8 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))

eval57.0ms (0.7%)

Memory: 28.4MiB live, 103.0MiB allocated
Compiler: Compiled 8 826 to 1 369 computations (84.5% saved)

prune63.0ms (0.8%)

Memory

-4.1MiB live, 114.8MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	394	9	403
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	394	10	404

Accuracy

99.9%

Counts

404 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	11.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	11.3%	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)))
▶	7.9%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	7.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.6%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
▶	3.8%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	9.3%	(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (fma.f64 x x x))))
▶	98.2%	#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))
	97.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 262 to 144 computations (45% saved)

simplify155.0ms (2%)

Memory

14.7MiB live, 164.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	320	(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	1088	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)))
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (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	(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))

Rules

14 042×	`lower-fma.f32`
14 040×	`lower-fma.f64`
3 182×	`lower--.f32`
3 176×	`lower--.f64`
2 650×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	205
0	48	207
1	85	195
2	219	179
3	467	179
4	1419	179
5	2870	179
6	7877	179
0	8240	176

Stop Event

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

Calls

Call 1

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

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

localize149.0ms (1.9%)

Memory

5.6MiB live, 168.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.20703125	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))
accuracy	21.96773016840555	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 #s(literal 1 binary64) x) x)))
accuracy	57.154950552421234	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.515625	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	58.91860046783495	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	1.8246276088033309	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy	58.91860046783495	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	58.91860046783495	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	59.496847198082065	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy	0.01953125	(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	0.140625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.265625	(/.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	0.8861969157311543	#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))

Samples

100.0ms	243×	1	valid
4.0ms	13×	0	valid

Compiler

Compiled 186 to 26 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

adjust: 25.0ms (31.5% of total)

ival-sqrt: 14.0ms (17.6% of total)

ival-mult: 13.0ms (16.4% of total)

ival-add: 11.0ms (13.9% of total)

ival-div: 10.0ms (12.6% of total)

ival-sub: 6.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

-16.5MiB live, 21.0MiB allocated

Counts

19 → 228

Calls

Call 1

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

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

3 calls:

Time

Variable

Point

Expression

7.0ms

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

2.0ms

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

simplify161.0ms (2.1%)

Memory

18.5MiB live, 167.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12 118×	`lower-fma.f64`
12 118×	`lower-fma.f32`
4 214×	`lower-+.f64`
4 214×	`lower-+.f32`
3 158×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	283	3219
1	849	2831
2	2671	2794
3	6740	2767
0	8134	2566

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 226

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

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

rewrite256.0ms (3.3%)

Memory

17.6MiB live, 335.0MiB allocated

Rules

4 558×	`lower-/.f32`
4 550×	`lower-/.f64`
4 542×	`lower-*.f32`
4 536×	`lower-*.f64`
3 334×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	172
0	48	168
1	221	152
2	2096	132
0	9174	126

Stop Event

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

Counts

19 → 1 406

Calls

Call 1

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

Outputs
#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))) x))
(.f64 (pow.f64 (/.f64 x (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(.f64 (.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (/.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))
(*.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 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64)))
(*.f64 (/.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))))
(*.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(pow.f64 (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64))) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (neg.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) #s(literal -1 binary64))) (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (neg.f64 x))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) (/.f64 #s(literal 1 binary64) x)) (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) x)
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x))) (neg.f64 (.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x)))) (neg.f64 (.f64 x (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64)) (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (neg.f64 x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64)) (.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (neg.f64 x)))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x))
(/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) x)) (.f64 x (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x) (/.f64 #s(literal -1/512 binary64) (.f64 (sqrt.f64 x) x))) (.f64 x (fma.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) x) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (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)))) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(neg.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (neg.f64 x)))
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(+.f64 (.f64 (sqrt.f64 x) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(+.f64 (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))
(+.f64 (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x) (.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) x)))
(+.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x))
(+.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 (+.f64 x x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(+.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x x)))
(*.f64 (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(*.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) x)))))
(.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x))) #s(literal -1 binary64))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (neg.f64 (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))))))
(/.f64 (-.f64 (.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x))) (*.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))
(/.f64 (neg.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x))) (neg.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x)))))
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x)) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x)))))
(/.f64 (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x)) (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))))
(/.f64 (*.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (-.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) x))) (fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 x) x))))
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 x))
(fma.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) (sqrt.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
(fma.f64 (+.f64 (neg.f64 x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))

eval631.0ms (8%)

Memory: -275.6MiB live, 578.3MiB allocated
Compiler: Compiled 96 228 to 6 902 computations (92.8% saved)

prune357.0ms (4.5%)

Memory

-11.0MiB live, 629.3MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	2 751	9	2 760
Fresh	4	0	4
Picked	3	2	5
Done	0	1	1
Total	2 758	12	2 770

Accuracy

100.0%

Counts

2 770 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.6%	(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
	29.6%	(/.f64 (.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x) (.f64 x (-.f64 x (+.f64 #s(literal 1 binary64) x)))) (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
▶	11.4%	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	7.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	4.6%	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
✓	3.8%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	18.8%	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
	97.1%	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (* (+ (sqrt x) (sqrt (+ 1 x))) (+ (+ 1 x) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
▶	98.2%	#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))) x))
▶	96.9%	#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))

Compiler

Compiled 321 to 169 computations (47.4% saved)

simplify210.0ms (2.7%)

Memory

18.1MiB live, 172.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	320	(*.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x))
cost-diff	384	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	576	(fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))
cost-diff	1088	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
cost-diff	0	(sqrt.f64 x)
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	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
cost-diff	0	#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))) 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))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #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)) (sqrt.f64 x))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Rules

24 538×	`lower-fma.f32`
24 530×	`lower-fma.f64`
3 868×	`lower-*.f32`
3 862×	`lower-*.f64`
2 914×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	266
0	65	252
1	96	237
2	200	231
3	411	231
4	1372	231
5	3138	231
0	8458	228

Stop Event

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

Calls

Call 1

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

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

localize203.0ms (2.6%)

Memory

-19.3MiB live, 210.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x)))
accuracy	0.2109375	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	21.96773016840555	(/.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (sqrt.f64 x))))
accuracy	57.154950552421234	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0.01953125	(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	0.265625	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
accuracy	0.29296875	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	0.8861969157311543	#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))) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.265625	(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy	0.8861969157311543	#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))
accuracy	1.7513117772699012	#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	58.91860046783495	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	59.47550027474127	#s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.02734375	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Samples

151.0ms	243×	1	valid
6.0ms	13×	0	valid

Compiler

Compiled 229 to 38 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-sqrt: 43.0ms (33.8% of total)

ival-add: 22.0ms (17.3% of total)

ival-div: 21.0ms (16.5% of total)

adjust: 17.0ms (13.3% of total)

ival-mult: 17.0ms (13.3% of total)

ival-sub: 6.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory

32.3MiB live, 32.3MiB allocated

Counts

21 → 252

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify172.0ms (2.2%)

Memory

1.9MiB live, 194.2MiB allocated

Algorithm

1×	egg-herbie

Rules

16 516×	`lower-fma.f64`
16 516×	`lower-fma.f32`
5 822×	`lower-+.f64`
5 822×	`lower-+.f32`
4 464×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	377	3602
1	1162	3191
2	3922	3145
0	8502	2910

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 250

Calls

Call 1

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

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

rewrite332.0ms (4.2%)

Memory

-7.0MiB live, 235.5MiB allocated

Rules

4 484×	`lower-*.f32`
4 478×	`lower-*.f64`
4 436×	`lower-/.f32`
4 426×	`lower-/.f64`
3 194×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	229
0	65	197
1	283	182
2	2326	174
0	8565	174

Stop Event

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

Counts

21 → 897

Calls

Call 1

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

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

eval256.0ms (3.3%)

Memory: 28.4MiB live, 319.3MiB allocated
Compiler: Compiled 46 361 to 3 915 computations (91.6% saved)

prune276.0ms (3.5%)

Memory

-45.6MiB live, 349.3MiB allocated

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	1 628	7	1 635
Fresh	4	0	4
Picked	2	3	5
Done	0	3	3
Total	1 634	13	1 647

Accuracy

100.0%

Counts

1 647 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.6%	(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	29.6%	(/.f64 (.f64 (fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)) (.f64 x (-.f64 x (+.f64 x #s(literal 1 binary64))))) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))))
	52.5%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	18.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)))
▶	96.9%	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
✓	7.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	4.6%	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	3.8%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	97.1%	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	98.2%	#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))) x))
✓	96.9%	#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))

Compiler

Compiled 286 to 158 computations (44.8% saved)

simplify162.0ms (2.1%)

Memory

-0.5MiB live, 186.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

16 336×	`lower-fma.f32`
16 334×	`lower-fma.f64`
3 308×	`lower--.f32`
3 306×	`lower--.f64`
2 864×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	224
0	58	219
1	98	198
2	215	196
3	433	196
4	1546	196
5	3200	196
6	7974	196
0	8364	193

Stop Event

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

Calls

Call 1

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

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

localize168.0ms (2.1%)

Memory

33.4MiB live, 270.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.02734375	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.20703125	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	21.96773016840555	(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
accuracy	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
accuracy	1.7533728679588463	#s(approx (+ (sqrt (+ 1 x)) (sqrt x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.02734375	(+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)))
accuracy	59.496847198082065	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	1.972114517937292	#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
accuracy	58.91860046783495	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
accuracy	59.47550027474127	#s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) 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	0.140625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	1.7447487711984104	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Samples

127.0ms	243×	1	valid
3.0ms	13×	0	valid

Compiler

Compiled 185 to 33 computations (82.2% saved)

Precisions

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

ival-mult: 36.0ms (36.7% of total)

ival-div: 19.0ms (19.3% of total)

adjust: 15.0ms (15.3% of total)

ival-add: 14.0ms (14.3% of total)

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

ival-sub: 4.0ms (4.1% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

-12.7MiB live, 25.7MiB allocated

Counts

19 → 228

Calls

Call 1

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

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

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify202.0ms (2.6%)

Memory

25.9MiB live, 221.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 582×	`lower-fma.f64`
15 582×	`lower-fma.f32`
6 338×	`lower-+.f64`
6 338×	`lower-+.f32`
4 042×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	346	3584
1	1060	3150
2	3541	3110
0	8274	2886

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

rewrite242.0ms (3.1%)

Memory

-17.6MiB live, 262.4MiB allocated

Rules

5 668×	`lower-/.f32`
5 660×	`lower-/.f64`
4 730×	`lower-*.f32`
4 722×	`lower-*.f64`
2 954×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	198
0	58	193
1	261	161
2	2173	153
0	9104	150

Stop Event

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

Counts

19 → 911

Calls

Call 1

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

Outputs
#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (log.f64 x)))
(.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))))))
(.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) x))))
(pow.f64 (/.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x)) (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x)))) (neg.f64 (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) x)))))
(/.f64 (-.f64 (.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))))) (.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) x)) (.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x))) (.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x)) (.f64 (sqrt.f64 x) x))) (.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x)) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) x))))
(/.f64 (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x))) (neg.f64 (-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x))) (neg.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x))) (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (-.f64 x (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x))) (neg.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) x))))
(/.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)) (-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 x))))
(/.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)) (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x)) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (-.f64 x (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 x))))))
(/.f64 (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x)) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x)) (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (neg.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (fma.f64 (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) x)) (fma.f64 (.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x)))) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ ( 1/2 x) 1) (.f64 #s(literal 1/2 binary64) x))) (.f64 (neg.f64 (sqrt.f64 x)) x))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 x) #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))))
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eval200.0ms (2.6%)

Memory: -2.9MiB live, 306.0MiB allocated
Compiler: Compiled 46 445 to 3 566 computations (92.3% saved)

prune244.0ms (3.1%)

Memory

7.3MiB live, 360.5MiB allocated

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	1 455	2	1 457
Fresh	1	1	2
Picked	2	3	5
Done	1	5	6
Total	1 459	11	1 470

Accuracy

100.0%

Counts

1 470 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.6%	(/.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (.f64 (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (fma.f64 #s(literal 4 binary64) (*.f64 x x) (-.f64 #s(literal 1 binary64) (+.f64 x x)))))
✓	65.6%	(/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	52.5%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))) (sqrt.f64 x)))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	7.9%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	4.6%	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	96.9%	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	97.1%	#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	98.2%	#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))) x))
✓	96.9%	#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))

Compiler

Compiled 552 to 181 computations (67.2% saved)

regimes16.0ms (0.2%)

Memory

28.5MiB live, 28.5MiB allocated

Counts

28 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	x
7.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes32.0ms (0.4%)

Memory

-35.1MiB live, 12.9MiB allocated

Counts

14 → 1

Calls

Call 1

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

Calls

2 calls:

28.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (* (+ (+ 1 x) x) (- (+ 1 x) x)) (+ (* (+ (* 2 x) 1) (sqrt (+ 1 x))) (* (+ (* 2 x) 1) (sqrt x)))) (/.f64 #s(literal 1/2 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
96.9%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
96.9%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
4.6%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

4.5MiB live, 4.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
1.6%	1	`x`
1.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	89
1	49	89
2	54	89
3	56	89
4	57	89

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.2s (14.9%)

Memory

-28.5MiB live, 690.9MiB allocated

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
16 516×	`lower-fma.f64`
16 516×	`lower-fma.f32`
12 118×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	198
0	58	193
1	261	161
2	2173	153
0	9104	150
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	377	3602
1	1162	3191
2	3922	3145
0	8502	2910
0	283	3219
1	849	2831
2	2671	2794
3	6740	2767
0	8134	2566
0	113	498
1	299	446
2	804	442
3	2258	434
4	4617	434
0	8205	398
0	29	172
0	48	168
1	221	152
2	2096	132
0	9174	126

Stop Event

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

Compiler

Compiled 256 to 104 computations (59.4% saved)

preprocess95.0ms (1.2%)

Memory: -15.9MiB live, 100.8MiB allocated
Compiler: Compiled 118 to 66 computations (44.1% 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%)

analyze2.0ms (0%)

sample1.4s (18.3%)

explain102.0ms (1.3%)

preprocess20.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize38.0ms (0.5%)

series5.0ms (0.1%)

simplify171.0ms (2.2%)

rewrite183.0ms (2.3%)

eval57.0ms (0.7%)

prune63.0ms (0.8%)

simplify155.0ms (2%)

localize149.0ms (1.9%)

series19.0ms (0.2%)

simplify161.0ms (2.1%)

rewrite256.0ms (3.3%)

eval631.0ms (8%)

prune357.0ms (4.5%)

simplify210.0ms (2.7%)

localize203.0ms (2.6%)

series18.0ms (0.2%)

simplify172.0ms (2.2%)

rewrite332.0ms (4.2%)

eval256.0ms (3.3%)

prune276.0ms (3.5%)

simplify162.0ms (2.1%)

localize168.0ms (2.1%)

series15.0ms (0.2%)

simplify202.0ms (2.6%)

rewrite242.0ms (3.1%)

eval200.0ms (2.6%)

prune244.0ms (3.1%)

regimes16.0ms (0.2%)

regimes32.0ms (0.4%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

simplify6.0ms (0.1%)

soundness1.2s (14.9%)

preprocess95.0ms (1.2%)

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