Metrics for 2sqrt (example 3.1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.5s (21.2%)

Memory

47.5MiB live, 1 945.0MiB allocated

Samples

1.1s	7 992×	1	valid
18.0ms	264×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 879.0ms

ival-sqrt: 324.0ms (36.9% of total)

const: 151.0ms (17.2% of total)

adjust: 141.0ms (16% of total)

ival-add: 106.0ms (12.1% of total)

ival-sub: 79.0ms (9% of total)

ival-<: 30.0ms (3.4% of total)

ival->: 25.0ms (2.8% of total)

ival-and: 13.0ms (1.5% of total)

exact: 8.0ms (0.9% of total)

ival-assert: 4.0ms (0.5% of total)

Bogosity

explain112.0ms (1.6%)

Memory

-2.0MiB live, 155.5MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	255	0

Confusion

	Predicted +	Predicted -
+	255	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	0
-	0	0	1

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms	496×	1	valid
1.0ms	16×	0	valid

Compiler

Compiled 65 to 34 computations (47.7% saved)

Precisions

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

ival-sqrt: 15.0ms (43.7% of total)

adjust: 8.0ms (23.3% of total)

ival-add: 6.0ms (17.5% of total)

ival-sub: 5.0ms (14.6% 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

6.0MiB live, 44.3MiB 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 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB 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)

localize36.0ms (0.5%)

Memory

-21.5MiB live, 60.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	59.80817911960563	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

29.0ms	248×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sqrt: 9.0ms (45.4% of total)

adjust: 4.0ms (20.2% of total)

ival-add: 4.0ms (20.2% of total)

ival-sub: 2.0ms (10.1% 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

7.1MiB live, 7.1MiB 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))

simplify160.0ms (2.3%)

Memory

10.0MiB live, 162.9MiB 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) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -5/128 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite177.0ms (2.5%)

Memory

12.1MiB live, 172.2MiB 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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 2 binary64)))) (-.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))) (fma.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (-.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(*.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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(*.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) x) x))
(*.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(*.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (pow.f64 (neg.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal -1 binary64)))
(*.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)) (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))))
(*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)))
(*.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)))
(.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (pow.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) #s(literal -1 binary64))))
(*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (pow.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 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 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) x))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))) (fma.f64 x (+.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) #s(literal -1 binary64))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (fma.f64 x x x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))) (+.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 (pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) 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 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (*.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 (pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x))))
(/.f64 (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (+.f64 (+.f64 (+.f64 (hypot.f64 (sqrt.f64 x) x) x) #s(literal 1 binary64)) x))
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
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(*.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 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #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 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))

eval50.0ms (0.7%)

Memory: -1.5MiB live, 72.1MiB allocated
Compiler: Compiled 7 571 to 1 407 computations (81.4% saved)

prune54.0ms (0.8%)

Memory

-29.2MiB live, 91.3MiB 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
	6.8%	(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))) (+.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))))))
	7.6%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	6.2%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	6.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.3%	(-.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))
▶	7.6%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
▶	98.5%	#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))
	98.0%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 279 to 158 computations (43.4% saved)

simplify233.0ms (3.3%)

Memory

53.9MiB live, 234.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

36 496×	`lower-fma.f32`
36 492×	`lower-fma.f64`
3 802×	`lower-*.f32`
3 798×	`lower-*.f64`
2 670×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	215
0	57	211
1	90	203
2	197	201
3	415	201
4	1478	201
5	5883	201
0	8315	198

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) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) x) x)
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(sqrt.f64 x)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
#s(literal 3/2 binary64)
(-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))
(+.f64 (+.f64 #s(literal 1 binary64) x) x)
(hypot.f64 (sqrt.f64 x) 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) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
(-.f64 (+.f64 #s(literal 1 binary64) x) x)
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(sqrt.f64 x)
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
#s(literal 3/2 binary64)
(-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))
(fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x)))
(+.f64 (+.f64 #s(literal 1 binary64) x) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))
(hypot.f64 (sqrt.f64 x) x)

localize169.0ms (2.4%)

Memory

0.9MiB live, 198.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
accuracy	0.8443816667058115	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))))
accuracy	20.326307794924	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
accuracy	59.57677049108313	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.48828125	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	59.80817911960563	(-.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	1.2283785996695267	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
accuracy	59.80817911960563	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	59.65169889909312	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy	59.80817911960563	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	0.00390625	(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	0.1328125	(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	0.686724290447476	#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

138.0ms	248×	1	valid
2.0ms	8×	0	valid

Compiler

Compiled 217 to 30 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-mult: 22.0ms (19.6% of total)

ival-pow: 17.0ms (15.1% of total)

adjust: 15.0ms (13.3% of total)

ival-sub: 14.0ms (12.5% of total)

ival-sqrt: 13.0ms (11.6% of total)

ival-add: 12.0ms (10.7% of total)

ival-div: 11.0ms (9.8% of total)

ival-hypot: 9.0ms (8% of total)

exact: 1.0ms (0.9% of total)

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

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

series77.0ms (1.1%)

Memory

-28.9MiB live, 62.5MiB allocated

Counts

17 → 204

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 #s(literal 1 binary64) x) x) (patch (-.f64 (+.f64 #s(literal 1 binary64) x) x) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) (patch (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<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>) () ())) ())
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#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf 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 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf 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 (+ (* -1/8 (* (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 (/.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>) () ())) ())
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#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
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#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>) () ())) ())
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#s(alt (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) (patch (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (taylor -inf x) (#s(alt (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) (patch (.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (patch (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) (patch (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

64.0ms

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

3.0ms

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

3.0ms

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

simplify180.0ms (2.6%)

Memory

1.6MiB live, 192.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 790×	`lower-fma.f64`
13 790×	`lower-fma.f32`
5 124×	`lower-*.f64`
5 124×	`lower-*.f32`
4 242×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	359	3625
1	1105	2869
2	3889	2801
0	8881	2591

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 202

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
1
1
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
1
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
1
(+ 1 (* x (+ 3/2 (sqrt x))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 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)))))
(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
1
1
1
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 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
1
1
1
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (/ (- (* -1 (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2))
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (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) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(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))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
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(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64))
(* -1 (/ (- (* -1 (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(-.f64 (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(-.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (*.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 0 binary64)) #s(literal 1/8 binary64)))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 0 binary64)) #s(literal 1/8 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)) #s(literal 0 binary64)) #s(literal -1/16 binary64) (fma.f64 (.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))) (.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64))))) (neg.f64 x)))) x)) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))) x) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) x)
(/ 1 (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/.f64 #s(literal -1 binary64) #s(literal 0 binary64))
(/ (+ (* -3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow x 2))
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)))
(/ (- (+ (* -3/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)))) (*.f64 x x))
(/ (- (+ (* -1 (/ (- (* -1 (/ (- (* -9/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* 1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (* -3/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 3))) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 3/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (pow x 2))
(fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) #s(literal -3/2 binary64) (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 #s(literal -3/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (/.f64 (fma.f64 #s(literal -9/4 binary64) x #s(literal 1 binary64)) #s(literal 0 binary64))) (sqrt.f64 x) (/.f64 (.f64 #s(literal 9/4 binary64) x) #s(literal 0 binary64)))) (*.f64 x x))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(literal 0 binary64)
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 (*.f64 x x) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 x x))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -9/4 binary64) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -3/2 binary64) (sqrt.f64 x))) (neg.f64 (pow.f64 x #s(literal 3 binary64))))) (.f64 x x))

rewrite167.0ms (2.4%)

Memory

29.3MiB live, 185.8MiB allocated

Rules

5 366×	`lower-*.f32`
5 362×	`lower-*.f64`
4 738×	`lower-fma.f32`
4 734×	`lower-fma.f64`
3 058×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	161
0	57	165
1	258	149
2	2380	137
0	8676	133

Stop Event

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

Counts

17 → 526

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

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) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/4 binary64) x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 x (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64)) (pow.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.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)))) #s(literal -1 binary64)))
(.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)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.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 (pow.f64 x #s(literal -1 binary64)) (pow.f64 (pow.f64 (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)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (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 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/4 binary64) x)) (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(/.f64 (.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 x #s(literal -1 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.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 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/4 binary64) x)) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/4 binary64) x)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.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 -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.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) (pow.f64 x #s(literal -1 binary64))) (.f64 #s(literal 1/4 binary64) x)) (.f64 x (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (fma.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (.f64 x (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal -1 binary64)) (-.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 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) (/.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)))
(exp.f64 (*.f64 (log.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)))
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(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

eval243.0ms (3.5%)

Memory: -58.3MiB live, 296.2MiB allocated
Compiler: Compiled 34 179 to 3 872 computations (88.7% saved)

prune187.0ms (2.7%)

Memory

25.4MiB live, 266.9MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	1 412	8	1 420
Fresh	3	1	4
Picked	3	2	5
Done	0	1	1
Total	1 418	12	1 430

Accuracy

100.0%

Counts

1 430 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.9%	(/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
	6.8%	(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))) (+.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))))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	6.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.3%	(-.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))
	98.0%	#s(approx (- (/ (+ 1 x) (sqrt (+ 1 x))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
▶	98.5%	#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))
▶	97.8%	#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))
	98.4%	#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))) (pow.f64 x #s(literal -1 binary64))))
▶	0.9%	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))

Compiler

Compiled 274 to 171 computations (37.6% saved)

simplify167.0ms (2.4%)

Memory

-13.3MiB live, 175.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

19 204×	`lower-fma.f32`
19 198×	`lower-fma.f64`
3 100×	`lower-*.f32`
3 096×	`lower-*.f64`
2 880×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	247
0	79	243
1	125	238
2	273	236
3	518	236
4	1746	236
5	4054	236
0	8227	233

Stop Event

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

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 x)
x
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64))
#s(literal -3 binary64)
#s(literal 0 binary64)
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #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 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
(-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x))
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(hypot.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
(*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(literal 3/2 binary64)

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

localize181.0ms (2.6%)

Memory

11.8MiB live, 148.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
accuracy	0	(-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0	(*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0	(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
accuracy	0	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	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))
accuracy	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	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))
accuracy	0	#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0	(/.f64 #s(literal -3 binary64) #s(literal 0 binary64))
accuracy	0	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
accuracy	0	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(sqrt.f64 x)

Samples

72.0ms

256×

invalid

Compiler

Compiled 238 to 43 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-div: 11.0ms (20.1% of total)

ival-add: 10.0ms (18.2% of total)

ival-mult: 10.0ms (18.2% of total)

ival-sqrt: 7.0ms (12.8% of total)

ival-pow: 6.0ms (10.9% of total)

ival-hypot: 5.0ms (9.1% of total)

ival-sub: 5.0ms (9.1% of total)

exact: 1.0ms (1.8% of total)

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

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

series23.0ms (0.3%)

Memory

-7.0MiB live, 28.6MiB allocated

Counts

19 → 216

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) (patch (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) #<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 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)) (patch (.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (patch (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) #<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 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt (/ 1 (+ 1 (sqrt x))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
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#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
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#s(alt (- (+ 1 (* 1/2 x)) (sqrt x)) (taylor 0 x) (#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ ( (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1/8 (sqrt (/ 1 (pow x 3)))) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) (patch (/.f64 #s(approx (+ ( (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) #<representation binary64>) () ())) ())
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#s(alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) (patch (/.f64 #s(approx (+ ( (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))) (patch (/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 3 x) (taylor -inf x) (#s(alt (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (patch (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- 1 (* 1/2 (pow (sqrt -1) 2))) x)) 3))) (taylor -inf x) (#s(alt (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (patch (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (+ 1 (* -1/8 (/ (pow (sqrt -1) 4) x))) (* 1/2 (pow (sqrt -1) 2))) x)) 3))) (taylor -inf x) (#s(alt (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (patch (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (- (+ 1 (* -1 (/ (- (* 1/16 (/ (pow (sqrt -1) 6) x)) (* -1/8 (pow (sqrt -1) 4))) x))) (* 1/2 (pow (sqrt -1) 2))) x)) 3))) (taylor -inf x) (#s(alt (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (patch (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#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 (* x (+ 2 (/ 1 x))) (taylor -inf x) (#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 (* x (+ 2 (/ 1 x))) (taylor -inf x) (#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 (* x (+ 2 (/ 1 x))) (taylor -inf x) (#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 x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1/8 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1/8 (sqrt (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (patch (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/ -3 0) (- (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))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1) (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ (* 2 x) 1) (+ 1 x) (/ -1/8 (sqrt x)))

5.0ms

-inf

((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/ -3 0) (- (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))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1) (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ (* 2 x) 1) (+ 1 x) (/ -1/8 (sqrt x)))

2.0ms

inf

((/ 1 (+ (sqrt x) (sqrt (+ 1 x)))) (+ (sqrt x) (sqrt (+ 1 x))) (sqrt x) (sqrt (+ 1 x)) (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/ -3 0) (- (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))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1) (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (+ (* 2 x) 1) (+ 1 x) (/ -1/8 (sqrt x)))

simplify167.0ms (2.4%)

Memory

2.5MiB live, 157.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 544×	`lower-fma.f64`
12 544×	`lower-fma.f32`
4 758×	`lower-*.f64`
4 758×	`lower-*.f32`
4 014×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	442	3885
1	1379	3119
2	4493	3060
0	8475	2845

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 213

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

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 (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ 1 (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)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) x (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (fma.f64 #s(literal 3/8 binary64) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) x (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (.f64 x x))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
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(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x)
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
#s(literal 0 binary64)
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (.f64 (*.f64 x x) #s(literal 3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (*.f64 x x))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 3/2 binary64) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 #s(literal -9/4 binary64) x #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -3/2 binary64) (sqrt.f64 x))) (neg.f64 (pow.f64 x #s(literal 3 binary64))))) (.f64 x x))
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64))
(* -1 (/ (- (* -1 (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(-.f64 (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)) (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 0 binary64))))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(-.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (*.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 0 binary64)) #s(literal 1/8 binary64)))) (/.f64 #s(literal 1/2 binary64) #s(literal 0 binary64))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(/.f64 (-.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 (fma.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64)) (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 0 binary64)) #s(literal 1/8 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)) #s(literal 0 binary64)) #s(literal -1/16 binary64) (fma.f64 (.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) #s(literal 0 binary64))) (.f64 #s(literal 9/2 binary64) (/.f64 (sqrt.f64 x) #s(literal 0 binary64))))) (neg.f64 x)))) x)) (/.f64 #s(literal 1/2 binary64) #s(literal 0 binary64))) x) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64))) x)
(* 3 x)
(*.f64 #s(literal 3 binary64) x)
(* -1 (* x (- (* -1 (/ (- 1 (* 1/2 (pow (sqrt -1) 2))) x)) 3)))
(*.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -3/2 binary64) x) #s(literal 3 binary64)) x)
(* -1 (* x (- (* -1 (/ (- (+ 1 (* -1/8 (/ (pow (sqrt -1) 4) x))) (* 1/2 (pow (sqrt -1) 2))) x)) 3)))
(*.f64 (neg.f64 x) (-.f64 #s(literal -3 binary64) (/.f64 (fma.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) x) #s(literal -1/8 binary64) #s(literal 3/2 binary64)) x)))
(* -1 (* x (- (* -1 (/ (- (+ 1 (* -1 (/ (- (* 1/16 (/ (pow (sqrt -1) 6) x)) (* -1/8 (pow (sqrt -1) 4))) x))) (* 1/2 (pow (sqrt -1) 2))) x)) 3)))
(.f64 (neg.f64 x) (-.f64 #s(literal -3 binary64) (/.f64 (fma.f64 (/.f64 (fma.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)) x) #s(literal 1/16 binary64))) x) #s(literal -1 binary64) #s(literal 3/2 binary64)) 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))
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))
(* -1/8 (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))

rewrite204.0ms (2.9%)

Memory

19.6MiB live, 248.7MiB allocated

Rules

5 196×	`lower-/.f32`
5 186×	`lower-/.f64`
4 018×	`lower-fma.f32`
4 012×	`lower-fma.f64`
3 642×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	52	207
0	79	184
1	342	161
2	2871	157
0	8931	157

Stop Event

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

Counts

19 → 1 235

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(/.f64 #s(literal -3 binary64) #s(literal 0 binary64))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
(/.f64 #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 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64))
(/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
(-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x))
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))

Outputs
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (pow.f64 (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x)))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) (/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x)))))
(*.f64 (/.f64 (+.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (hypot.f64 (sqrt.f64 x) x) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 x x x))) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) (/.f64 (fma.f64 #s(literal 2 binary64) x (-.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) (+.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 (hypot.f64 (sqrt.f64 x) x) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (fma.f64 x x x)))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) (.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))))) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) (/.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x x) #s(literal 3/2 binary64)))) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x x x)) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x (+.f64 #s(literal 1 binary64) (hypot.f64 (sqrt.f64 x) x))) #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)))))
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(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (*.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(/.f64 (exp.f64 (log1p.f64 (*.f64 (neg.f64 x) x))) (exp.f64 (log1p.f64 (neg.f64 x))))
(/.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (exp.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64)))) (exp.f64 (log1p.f64 (fma.f64 x x (neg.f64 x)))))
(/.f64 (exp.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64)))) (exp.f64 (log.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))))
(/.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 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64))
(sqrt.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64)))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(fabs.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (log1p.f64 x))
(*.f64 #s(literal 1/8 binary64) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #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)))

eval267.0ms (3.8%)

Memory: 27.9MiB live, 327.9MiB allocated
Compiler: Compiled 49 769 to 4 131 computations (91.7% saved)

prune208.0ms (3%)

Memory

-15.7MiB live, 297.8MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	1 697	9	1 706
Fresh	3	1	4
Picked	2	3	5
Done	2	1	3
Total	1 704	14	1 718

Accuracy

100.0%

Counts

1 718 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.9%	(/.f64 (fma.f64 (/.f64 x (sqrt.f64 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
	52.3%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 x)))
	52.3%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
▶	52.3%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	18.8%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
▶	97.8%	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
✓	6.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.3%	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
	98.0%	#s(approx (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	98.5%	#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))
✓	97.8%	#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))
▶	98.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
▶	3.8%	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

Compiler

Compiled 273 to 204 computations (25.3% saved)

simplify108.0ms (1.5%)

Memory

17.6MiB live, 131.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
cost-diff	384	(/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x 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 x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
cost-diff	0	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
cost-diff	0	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
cost-diff	128	(neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
cost-diff	1152	(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))

Rules

7 022×	`lower-fma.f32`
7 018×	`lower-fma.f64`
2 842×	`lower-*.f32`
2 838×	`lower-*.f64`
1 992×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	235
0	69	231
1	119	225
2	285	219
3	760	204
4	2595	200
5	7287	200
0	8136	195

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.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)))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
#s(literal -1/8 binary64)
(/.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
#s(literal 0 binary64)
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))
(sqrt.f64 x)
x
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
#s(literal 1 binary64)
#s(approx (+ (sqrt x) (sqrt (+ 1 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 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))
(sqrt.f64 x)
x
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(-.f64 x #s(literal 1 binary64))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)

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

localize513.0ms (7.3%)

Memory

-379.3MiB live, 263.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.13671875	(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
accuracy	0.26953125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
accuracy	29.633816938996652	(/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
accuracy	1.1854958899289432	#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.00390625	(+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))
accuracy	0.24609375	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
accuracy	59.65169889909312	#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
accuracy	61.54169312408547	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
accuracy	0.00390625	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
accuracy	0.234375	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
accuracy	0.33984375	(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))
accuracy	0.686724290447476	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))

Samples

480.0ms	248×	1	valid
2.0ms	8×	0	valid

Compiler

Compiled 214 to 42 computations (80.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 450.0ms

ival-sqrt: 331.0ms (73.6% of total)

ival-div: 29.0ms (6.4% of total)

ival-add: 19.0ms (4.2% of total)

adjust: 19.0ms (4.2% of total)

ival-mult: 16.0ms (3.6% of total)

ival-pow: 14.0ms (3.1% of total)

ival-hypot: 10.0ms (2.2% of total)

ival-sub: 8.0ms (1.8% of total)

ival-neg: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series19.0ms (0.3%)

Memory

29.7MiB live, 29.7MiB allocated

Counts

18 → 216

Calls

Call 1

Inputs
#s(alt (.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)) (patch (.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)) #<representation binary64>) () ())
#s(alt (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (patch (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))) (patch #s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (patch (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64)) (patch #s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) (patch (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (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 (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (.f64 #s(literal 2 binary64) (sqrt.f64 x)))) (patch (/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (.f64 #s(literal 2 binary64) (sqrt.f64 x)))) #<representation binary64>) () ())
#s(alt #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (patch #s(approx (+ (sqrt x) (sqrt (+ 1 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 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (patch (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) (patch (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (patch (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) #<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 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (patch (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())

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

3 calls:

Time

Variable

Point

Expression

5.0ms

-inf

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

4.0ms

inf

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

2.0ms

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

simplify157.0ms (2.2%)

Memory

11.3MiB live, 159.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12 264×	`lower-fma.f64`
12 264×	`lower-fma.f32`
4 484×	`lower-*.f64`
4 484×	`lower-*.f32`
3 224×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	480	4250
1	1458	3456
2	5177	3401
0	8311	3175

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/8 (sqrt (/ 1 x)))
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (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))))))
(sqrt x)
(sqrt x)
(sqrt x)
(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 (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 (* -1 x))
(+ 1 (* x (- x 1)))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ 1 (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))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 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 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (sqrt x))
(* x (- (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (- (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (- (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) 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)
(sqrt x)
(sqrt x)
(sqrt 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)
(* 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 x)
(/ (- 1 (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (/ 1 x)) x)
(/ (- (+ 1 (/ 1 (pow x 2))) (+ (/ 1 x) (/ 1 (pow x 3)))) 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)))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (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 (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (- (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(/ 3 (* x (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (/ (- (* -1 (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x))
(* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/16 (/ (pow (sqrt -1) 6) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* 3/2 (* (sqrt x) (/ (- (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* 9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))))) x)) (* 1/8 (/ (pow (sqrt -1) 4) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (* -9/2 (* (sqrt x) (/ 1 (pow (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) x)) (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (* 1/2 (/ (pow (sqrt -1) 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 3 (/ 1 (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -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 (* (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 (* 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))
(* -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 x)
(* -1 (/ (- (/ 1 x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
(/ -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))) x))
(* -1 (/ (- (+ (/ 1/16 (* (pow x 4) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 11))) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))))) x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1 (sqrt x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- 1 (* -1/4 x))))) (* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))

Outputs
(* -1/8 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
(* 1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x)
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x)
(/ (- (* -1/2 (sqrt (pow x 3))) (* -1/8 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 #s(literal 1/2 binary64) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) x (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (fma.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) (fma.f64 #s(literal 3/8 binary64) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (*.f64 #s(literal -3/8 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))) x (fma.f64 (+.f64 #s(literal -1 binary64) (sqrt.f64 x)) (+.f64 #s(literal 3/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (/.f64 x (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ 1 (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 x #s(literal -1/8 binary64) #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)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 x #s(literal -1/8 binary64) #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 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (/.f64 x (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ 1 (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 x #s(literal -1/8 binary64) #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)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- x 1)))
(fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(fma.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (/.f64 x (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64))))) x (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))) x (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(+ 1 (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 x #s(literal -1/8 binary64) #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)))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
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(* -1 (/ (- (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))) x))
(/.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/4 binary64) #s(literal 0 binary64)))) (neg.f64 x))
(* -1 (/ (- (+ (/ 1/16 (* (pow x 4) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (/ 1 (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 11))) (/ (- (* -1/4 (/ x (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2))))) (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 2)))) (* 1/4 (/ 1 (* (pow x 3) (* (pow (sqrt -1) 2) (pow (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 3)))))))))) x))
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64))) (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 0 binary64)) (.f64 (fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64)) #s(literal 1/8 binary64) (.f64 (/.f64 x #s(literal 0 binary64)) #s(literal -1/4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))))) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 0 binary64)) #s(literal -1/8 binary64) (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal 0 binary64)) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) #s(literal 0 binary64)))))) (neg.f64 x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
#s(literal 0 binary64)
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) x)
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* -1/16 (sqrt (/ 1 (pow x 7)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(.f64 (fma.f64 #s(literal -1 binary64) (+.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) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (neg.f64 x))
(* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7)))))))))
(.f64 (+.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) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (- 1 (* -1/4 x))))) (* 1/2 (* (sqrt x) (pow (sqrt -1) 2)))) (pow x 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

rewrite173.0ms (2.5%)

Memory

7.6MiB live, 227.9MiB allocated

Rules

5 668×	`lower-*.f32`
5 664×	`lower-*.f64`
3 924×	`lower-fma.f32`
3 920×	`lower-fma.f64`
3 510×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	206
0	69	202
1	328	160
2	2945	148
0	9703	145

Stop Event

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

Counts

18 → 519

Calls

Call 1

Inputs
(*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
(+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)))
(sqrt.f64 x)
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
#s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
(+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))))

Outputs
(.f64 (.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(*.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(.f64 #s(literal -1 binary64) (.f64 (pow.f64 x #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.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))) (/.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))) (neg.f64 (/.f64 #s(literal -1 binary64) x)))
(pow.f64 (/.f64 x (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (neg.f64 x))
(/.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))) (neg.f64 x))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) x)
(/.f64 #s(literal 1 binary64) (/.f64 x (neg.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (*.f64 x #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (neg.f64 x))
(neg.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) x))
(+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x)) (*.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) x)))
(+.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(*.f64 #s(literal -1 binary64) (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))) #s(literal -1 binary64))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 2 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/8 binary64) (.f64 #s(literal 1/512 binary64) (pow.f64 x #s(literal -3/2 binary64)))) (fma.f64 #s(literal 1/4 binary64) x (-.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x))) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1/4 binary64) x) (/.f64 #s(literal 1/64 binary64) x)) (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/4 binary64) x (/.f64 #s(literal 1/64 binary64) x)) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(fma.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -1/2 binary64)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1 binary64) (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) #s(literal -1 binary64) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1/8 binary64) (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))
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(fma.f64 #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))
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(*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal -1 binary64))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal -1 binary64)))))
(*.f64 (pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal -1 binary64)))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(pow.f64 (exp.f64 (neg.f64 (log1p.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))) (hypot.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x))
(/.f64 (sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))) (sqrt.f64 (+.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (fma.f64 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)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log1p.f64 x) #s(literal 1/2 binary64))))

eval152.0ms (2.2%)

Memory: -30.2MiB live, 257.4MiB allocated
Compiler: Compiled 15 769 to 2 715 computations (82.8% saved)

prune114.0ms (1.6%)

Memory

5.1MiB live, 244.6MiB allocated

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	856	3	859
Fresh	1	4	5
Picked	2	3	5
Done	0	4	4
Total	859	14	873

Accuracy

100.0%

Counts

873 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.9%	(/.f64 (fma.f64 (/.f64 x (sqrt.f64 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
	52.3%	(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 x)))
	52.3%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))))
✓	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	18.8%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
✓	97.8%	(/.f64 #s(literal 1 binary64) #s(approx (+ (sqrt x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (sqrt.f64 x))))
✓	6.5%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.3%	(-.f64 #s(approx (/ (+ 1 x) (sqrt (+ 1 x))) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
	98.0%	#s(approx (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	98.5%	#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))
✓	97.8%	#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))
	98.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) x)))
✓	3.8%	#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

Compiler

Compiled 525 to 229 computations (56.4% saved)

regimes17.0ms (0.2%)

Memory

33.1MiB live, 33.1MiB allocated

Counts

30 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (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))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 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(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (/ (+ 1 x) (sqrt (+ 1 x))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (*.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 x) (sqrt (+ 1 x))) (*.f64 #s(literal 2 binary64) (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) (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 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
#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))) (pow.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))) (sqrt.f64 x)))
(/.f64 (fma.f64 (/.f64 x (sqrt.f64 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x #s(literal 1 binary64))) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
(/.f64 (-.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (hypot.f64 (sqrt.f64 x) x)) (*.f64 (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (sqrt.f64 x) x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (hypot.f64 (sqrt.f64 x) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)) (pow.f64 (/.f64 x (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64))) (+.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))))))

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

Calls

2 calls:

9.0ms	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 8 to 7 computations (12.5% saved)

regimes12.0ms (0.2%)

Memory

-22.0MiB live, 16.5MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (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))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 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(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (- (/ (+ 1 x) (sqrt (+ 1 x))) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
#s(approx (/ (- (+ (* 2 x) 1) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x)))) (* (+ (* (sqrt x) x) (pow (+ 1 x) 3/2)) 1)) (*.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 x) (sqrt (+ 1 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:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
4.0ms	x

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (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))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
18.8%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
18.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (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))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.3%	1	`x`
4.3%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes7.0ms (0.1%)

Memory

-30.8MiB live, 7.9MiB allocated

Accuracy

Total -1.9b remaining (-3.1%)

Threshold costs -1.9b (-3.1%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) (/.f64 #s(literal -3 binary64) #s(literal 0 binary64)))

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

Outputs
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
3.8%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
3.8%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify25.0ms (0.4%)

Memory

7.8MiB live, 46.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative-binary64-+.f64`
4×	`-commutative-binary64-.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	81
1	47	81
2	51	81
3	53	81
4	54	81

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 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(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (sqrt.f64 x)))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (/ (- (+ 1 x) x) (+ (* (sqrt x) x) (pow (+ 1 x) 3/2))) (- (+ (+ 1 x) x) (sqrt (+ (* (sqrt x) (sqrt x)) (* x x))))) #s(literal 0 binary64))

soundness1.0s (14.4%)

Memory

-7.1MiB live, 641.3MiB allocated

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
13 790×	`lower-fma.f64`
13 790×	`lower-fma.f32`
12 544×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	207
0	79	184
1	342	161
2	2871	157
0	8931	157
0	32	161
0	57	165
1	258	149
2	2380	137
0	8676	133
0	442	3885
1	1379	3119
2	4493	3060
0	8475	2845
0	359	3625
1	1105	2869
2	3889	2801
0	8881	2591
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	113	498
1	299	446
2	804	442
3	2258	434
4	4617	434
0	8205	398

Stop Event

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

Compiler

Compiled 161 to 88 computations (45.3% saved)

preprocess123.0ms (1.8%)

Memory: -0.7MiB live, 115.9MiB allocated
Compiler: Compiled 90 to 62 computations (31.1% 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%)

sample1.5s (21.2%)

explain112.0ms (1.6%)

preprocess20.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize36.0ms (0.5%)

series5.0ms (0.1%)

simplify160.0ms (2.3%)

rewrite177.0ms (2.5%)

eval50.0ms (0.7%)

prune54.0ms (0.8%)

simplify233.0ms (3.3%)

localize169.0ms (2.4%)

series77.0ms (1.1%)

simplify180.0ms (2.6%)

rewrite167.0ms (2.4%)

eval243.0ms (3.5%)

prune187.0ms (2.7%)

simplify167.0ms (2.4%)

localize181.0ms (2.6%)

series23.0ms (0.3%)

simplify167.0ms (2.4%)

rewrite204.0ms (2.9%)

eval267.0ms (3.8%)

prune208.0ms (3%)

simplify108.0ms (1.5%)

localize513.0ms (7.3%)

series19.0ms (0.3%)

simplify157.0ms (2.2%)

rewrite173.0ms (2.5%)

eval152.0ms (2.2%)

prune114.0ms (1.6%)

regimes17.0ms (0.2%)

regimes12.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes7.0ms (0.1%)

simplify25.0ms (0.4%)

soundness1.0s (14.4%)

preprocess123.0ms (1.8%)

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