Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Memory

3.7MiB live, 3.7MiB 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)

sample1.7s (18.6%)

Memory

-173.4MiB live, 1 892.3MiB allocated

Samples

1.3s	7 999×	1	valid
17.0ms	257×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sqrt: 521.0ms (48.9% of total)

adjust: 160.0ms (15% of total)

const: 128.0ms (12% of total)

ival-add: 98.0ms (9.2% of total)

ival-sub: 82.0ms (7.7% of total)

ival-<: 31.0ms (2.9% of total)

ival->: 23.0ms (2.2% of total)

ival-and: 11.0ms (1% of total)

exact: 7.0ms (0.7% of total)

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

Bogosity

preprocess28.0ms (0.3%)

Memory

-15.6MiB live, 21.4MiB 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))

explain140.0ms (1.6%)

Memory

-2.1MiB live, 117.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(-.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	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	256	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms	504×	1	valid
0.0ms	8×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sqrt: 14.0ms (42.3% of total)

adjust: 8.0ms (24.2% of total)

ival-add: 5.0ms (15.1% of total)

ival-sub: 5.0ms (15.1% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

localize60.0ms (0.7%)

Memory

-4.8MiB live, 69.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

27.0ms	252×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sqrt: 9.0ms (49.8% of total)

adjust: 4.0ms (22.1% of total)

ival-add: 3.0ms (16.6% of total)

ival-sub: 2.0ms (11.1% 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

17.6MiB live, 17.6MiB 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 (* 1/2 (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 (* -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 (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 (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 (* -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 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 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 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 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())

Calls

12 calls:

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

simplify425.0ms (4.8%)

Memory

-3.6MiB live, 718.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	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))
(* 1/2 (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 (/ (+ (* -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
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

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

rewrite299.0ms (3.3%)

Memory

-2.9MiB live, 433.7MiB allocated

Algorithm

1×	batch-egg-rewrite

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
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(+.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 0 binary64)) (sqrt.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (+.f64 x #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (+.f64 x (-.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))) (+.f64 x (-.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (*.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))))) (sqrt.f64 (fma.f64 x (.f64 x (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)))) (sqrt.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) x)) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
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(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x)))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (sqrt.f64 (.f64 (+.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)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (sqrt.f64 (sqrt.f64 x)))

eval50.0ms (0.6%)

Memory: 17.0MiB live, 89.8MiB allocated
Compiler: Compiled 8 826 to 1 381 computations (84.4% saved)

prune64.0ms (0.7%)

Memory

-2.3MiB live, 120.5MiB 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
	7.2%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	7.2%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
▶	5.5%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	4.4%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #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))
	5.1%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	99.3%	#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))
	98.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 266 to 152 computations (42.9% saved)

simplify312.0ms (3.5%)

Memory

-5.0MiB live, 348.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	320	(.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
✓	cost-diff	384	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	1472	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
✓	cost-diff	0	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.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)
✓	cost-diff	0	#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))

Rules

11 288×	`lower-fma.f32`
11 286×	`lower-fma.f64`
3 584×	`lower-+.f32`
3 578×	`lower-+.f64`
3 498×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	227
0	54	247
1	87	241
2	194	211
3	842	191
4	4739	191
0	8209	188

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

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

localize144.0ms (1.6%)

Memory

32.7MiB live, 228.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.5%	(.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
✓	accuracy	6.5%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.2%	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	5.6%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	98.8%	#s(approx (sqrt (+ x 1)) (sqrt.f64 x))
✓	accuracy	5.6%	(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	6.9%	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
✓	accuracy	5.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	#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))
✓	accuracy	99.6%	(/.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)

Samples

91.0ms	252×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 208 to 26 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-div: 14.0ms (21.7% of total)

adjust: 12.0ms (18.6% of total)

ival-add: 12.0ms (18.6% of total)

ival-sqrt: 10.0ms (15.5% of total)

ival-mult: 9.0ms (13.9% of total)

ival-sub: 7.0ms (10.8% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

-14.9MiB live, 25.4MiB allocated

Counts

18 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
1.0ms	x	@	inf	(* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
1.0ms	x	@	-inf	(/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1)))
1.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
1.0ms	x	@	0	(* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))

simplify427.0ms (4.8%)

Memory

-9.2MiB live, 521.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 524×	`lower-fma.f64`
15 524×	`lower-fma.f32`
4 290×	`lower-*.f64`
4 290×	`lower-*.f32`
3 456×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	3352
1	750	2964
2	2277	2912
3	7143	2906
0	8278	2704

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 214

Calls

Call 1

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

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

rewrite372.0ms (4.2%)

Memory

10.8MiB live, 485.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 588×	`lower-/.f32`
5 578×	`lower-/.f64`
4 770×	`lower-*.f32`
4 764×	`lower-*.f64`
3 126×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	179
0	54	167
1	224	151
2	1948	151
0	9307	144

Stop Event

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

Counts

18 → 1 093

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x))
(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)))
(-.f64 (/.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x) (/.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) (neg.f64 x)))
(-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 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)))
(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))
(/.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)))))
(/.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) (neg.f64 (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64))))
(/.f64 (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 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (.f64 x (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x))
(/.f64 (.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal -1 binary64)) (.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (neg.f64 x)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) (neg.f64 (.f64 x (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64)))) (neg.f64 (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #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)) 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 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x)) (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) #s(literal -1 binary64))) (neg.f64 (.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (neg.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (neg.f64 x))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64))) (neg.f64 x))
(/.f64 (neg.f64 (*.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(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))
(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))
(*.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))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64)))
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(pow.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (sqrt.f64 x) (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x))))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (*.f64 x (sqrt.f64 x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x x)))))

eval272.0ms (3%)

Memory: 29.4MiB live, 395.2MiB allocated
Compiler: Compiled 67 774 to 6 173 computations (90.9% saved)

prune296.0ms (3.3%)

Memory

-9.8MiB live, 438.1MiB allocated

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	2 004	11	2 015
Fresh	3	1	4
Picked	2	3	5
Done	0	1	1
Total	2 009	16	2 025

Accuracy

100.0%

Counts

2 025 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.2%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	98.3%	(/.f64 (.f64 #s(approx ( (+ x (+ x 1)) (+ x (- 1 x))) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
▶	99.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
▶	98.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	5.5%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	4.4%	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #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))
	3.5%	(.f64 (/.f64 (.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	18.8%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
	98.7%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	66.2%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
▶	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
	99.1%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.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))))))
▶	34.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))))

Compiler

Compiled 415 to 242 computations (41.7% saved)

simplify289.0ms (3.2%)

Memory

-8.9MiB live, 339.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (*.f64 (sqrt.f64 x) #s(literal -1/8 binary64)))
✓	cost-diff	(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
✓	cost-diff	#s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x)))
✓	cost-diff	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))))
✓	cost-diff	(+.f64 x (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x))
✓	cost-diff	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	cost-diff	#s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	cost-diff	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	#s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	cost-diff	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 x))
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))
✓	cost-diff	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x)))
✓	cost-diff	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))

Rules

9 434×	`lower-fma.f32`
9 428×	`lower-fma.f64`
4 196×	`lower--.f32`
4 194×	`lower--.f64`
2 622×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	385
0	72	373
1	113	365
2	205	341
3	740	341
4	3970	341
5	7434	341
0	8654	328

Stop Event

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

Calls

Call 1

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

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

localize200.0ms (2.2%)

Memory

6.7MiB live, 282.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))))
✓	accuracy	71.3%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	50.4%	(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	98.9%	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
✓	accuracy	99.6%	(/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	98.9%	#s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	6.9%	#s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
✓	accuracy	5.6%	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))
✓	accuracy	99.9%	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))

Samples

133.0ms	252×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 280 to 38 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 103.0ms

ival-div: 22.0ms (21.4% of total)

ival-add: 22.0ms (21.4% of total)

ival-mult: 22.0ms (21.4% of total)

adjust: 17.0ms (16.6% of total)

ival-sqrt: 12.0ms (11.7% of total)

ival-sub: 7.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

66 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (* x x))
0.0ms	x	@	-inf	(/ (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (* x x))
0.0ms	x	@	inf	(/ (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (* x x))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(+ (* (sqrt (/ 1 x)) 1/4) (sqrt x))

simplify404.0ms (4.5%)

Memory

9.6MiB live, 608.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 422×	`lower-fma.f64`
11 422×	`lower-fma.f32`
3 580×	`lower-+.f64`
3 580×	`lower-+.f32`
3 458×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	270	3745
1	809	3283
2	2517	3238
3	6793	3222
0	8416	3031

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 262

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

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

rewrite323.0ms (3.6%)

Memory

19.4MiB live, 407.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 286×	`lower-/.f32`
5 276×	`lower-/.f64`
4 386×	`lower-*.f32`
4 378×	`lower-*.f64`
2 848×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	346
0	72	326
1	281	283
2	2223	275
0	8574	263

Stop Event

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

Counts

22 → 474

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))) (/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(neg.f64 (/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(neg.f64 (/.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(/.f64 (.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(pow.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))))
(.f64 (neg.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (fma.f64 x (.f64 x x) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x x)))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (fma.f64 x (.f64 x x) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x x)))))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal -1 binary64)) x))) (-.f64 (+.f64 x #s(literal -1 binary64)) x))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64)) (-.f64 (+.f64 x #s(literal -1 binary64)) x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x #s(literal -1 binary64)) x))))
#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))
(+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64)) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64)) (-.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/4 binary64) (sqrt.f64 x))
(fma.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) x) #s(literal 1/4 binary64)) (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64)) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) x) #s(literal 1/4 binary64)) (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64)) x))))
(/.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))) (-.f64 (fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (.f64 x (sqrt.f64 x)))) (+.f64 x (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64)) #s(literal 1/4 binary64))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64))) (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))))
(/.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64))) (fma.f64 x #s(literal 1/64 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))))))
(/.f64 (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64))) (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)))) (neg.f64 (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)))) (neg.f64 (fma.f64 x #s(literal 1/64 binary64) (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64)))) (neg.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (.f64 x #s(literal 1/64 binary64)) (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (.f64 x #s(literal 1/64 binary64)))) (.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64))))) (neg.f64 (neg.f64 (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x #s(literal 1/64 binary64)) (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))))) (neg.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))))
(pow.f64 (/.f64 (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (*.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64)))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/8 binary64)) (.f64 x (.f64 x x)) (.f64 (.f64 x (sqrt.f64 x)) #s(literal -1/512 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 x #s(literal 1/64 binary64))) (.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))))
(.f64 (-.f64 (.f64 x (.f64 #s(literal 1/4 binary64) (.f64 x x))) (.f64 x #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 x) (.f64 x #s(literal 1/2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(exp.f64 (log1p.f64 x))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal 2 binary64)))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(fabs.f64 (+.f64 x #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.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))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))))
(/.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) (neg.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.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 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #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 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #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 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (.f64 x 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)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #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 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (-.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)))))
(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))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) #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))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(fabs.f64 (*.f64 x (sqrt.f64 x)))
(sqrt.f64 (.f64 x (.f64 x x)))
(pow.f64 x #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(*.f64 x (sqrt.f64 x))
(*.f64 (sqrt.f64 x) x)
(.f64 (.f64 x (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (.f64 x (sqrt.f64 x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 (*.f64 x (sqrt.f64 x))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64) (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)))
(/.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(/.f64 (neg.f64 (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(.f64 x (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))

eval136.0ms (1.5%)

Memory: -32.5MiB live, 219.3MiB allocated
Compiler: Compiled 21 234 to 1 939 computations (90.9% saved)

prune124.0ms (1.4%)

Memory

14.4MiB live, 216.7MiB allocated

Pruning

18 alts after pruning (12 fresh and 6 done)

	Pruned	Kept	Total
New	993	8	1 001
Fresh	3	4	7
Picked	3	2	5
Done	0	4	4
Total	999	18	1 017

Accuracy

100.0%

Counts

1 017 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.2%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
▶	99.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
	98.4%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))))
✓	98.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
	18.8%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x #s(approx (+ x 1) #s(literal 1 binary64))))
	5.3%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) #s(approx (+ x (+ x 1)) #s(literal 1 binary64)))
✓	5.5%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	4.4%	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 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))
	3.5%	(.f64 (/.f64 (.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
▶	18.8%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	98.7%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
	98.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1 binary64) (/.f64 x #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))
	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (/.f64 #s(approx (+ ( -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
▶	33.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))))

Compiler

Compiled 382 to 207 computations (45.8% saved)

simplify348.0ms (3.9%)

Memory

-20.0MiB live, 338.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Program
✓	cost-diff	#s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
✓	cost-diff	(/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))
✓	cost-diff	#s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x)))
✓	cost-diff	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))))
✓	cost-diff	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	#s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	#s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 x))
✓	cost-diff	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))
✓	cost-diff	(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))
✓	cost-diff	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
✓	cost-diff	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))

Rules

11 382×	`lower-fma.f64`
11 382×	`lower-fma.f32`
3 592×	`lower-+.f32`
3 584×	`lower-+.f64`
3 444×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	401
0	80	379
1	124	371
2	230	347
3	866	327
4	4796	327
0	8224	314

Stop Event

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

Calls

Call 1

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

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

localize219.0ms (2.4%)

Memory

5.9MiB live, 321.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))))
✓	accuracy	98.9%	#s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
✓	accuracy	71.3%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	50.4%	(/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.9%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	18.8%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	98.7%	#s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	6.9%	#s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64))))
✓	accuracy	5.6%	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))
✓	accuracy	99.9%	#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
✓	accuracy	99.6%	(/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))

Samples

148.0ms	252×	1	valid
1.0ms	4×	0	valid

Compiler

Compiled 263 to 41 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 102.0ms

ival-div: 22.0ms (21.6% of total)

ival-mult: 22.0ms (21.6% of total)

ival-add: 19.0ms (18.6% of total)

adjust: 18.0ms (17.7% of total)

ival-sqrt: 12.0ms (11.8% of total)

ival-sub: 7.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series18.0ms (0.2%)

Memory

-11.2MiB live, 29.7MiB allocated

Counts

21 → 252

Calls

Call 1

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

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

Calls

63 calls:

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

simplify533.0ms (6%)

Memory

30.0MiB live, 582.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 972×	`lower-fma.f64`
14 972×	`lower-fma.f32`
4 332×	`lower-*.f64`
4 332×	`lower-*.f32`
3 286×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	296	3365
1	893	2993
2	2764	2960
3	7880	2958
0	8723	2790

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

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

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

rewrite304.0ms (3.4%)

Memory

-31.1MiB live, 461.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 492×	`lower-/.f32`
4 482×	`lower-/.f64`
4 404×	`lower-*.f32`
4 394×	`lower-*.f64`
3 062×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	361
0	80	335
1	307	293
2	2424	285
0	8570	269

Stop Event

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

Counts

21 → 283

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))))))
(neg.f64 (/.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64))))
(/.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))) (neg.f64 (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))))) (neg.f64 (neg.f64 (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) #s(literal 1 binary64))) (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(pow.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (neg.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal 1 binary64)))) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 x #s(literal 1 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (fma.f64 x (.f64 x x) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x x)))
(.f64 (/.f64 #s(approx ( (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))) (*.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (-.f64 x (+.f64 x #s(literal 1 binary64))))) (-.f64 x (+.f64 x #s(literal 1 binary64))))
#s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))
(+.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 x (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(fma.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/4 binary64) (sqrt.f64 x))
(fma.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))) (sqrt.f64 x))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64))) (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64))) (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) x))))
(/.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64))))
(/.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))) (+.f64 x (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/4 binary64))))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) x) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x))))) (neg.f64 (+.f64 x (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) x)) (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(/.f64 (-.f64 x (/.f64 #s(literal 1/16 binary64) x)) (-.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/16 binary64) x) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) x)) (*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x)))))) (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) x))) (neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 x (/.f64 #s(literal 1/16 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 x) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)))))
(pow.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64))) (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (*.f64 x (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (/.f64 #s(literal 1/16 binary64) x) x)) #s(literal -1 binary64))
(.f64 (fma.f64 x (sqrt.f64 x) (/.f64 #s(literal 1/64 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) (+.f64 x #s(literal -1/4 binary64)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) x) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1/4 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (sqrt.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 4 binary64)))))
(/.f64 #s(literal 1/4 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/4 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal 4 binary64))))
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(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x))) #s(literal -1 binary64))
(/.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))))
(/.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)) (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x)))))
(/.f64 (+.f64 x #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) (neg.f64 (+.f64 x (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))))))
(/.f64 (neg.f64 (+.f64 x #s(literal -1 binary64))) (neg.f64 (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (fma.f64 x (sqrt.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 x)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (sqrt.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 #s(literal -1 binary64)))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(exp.f64 (neg.f64 (log.f64 x)))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 x))))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 (neg.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (*.f64 x x))))
#s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (*.f64 x (neg.f64 x))))
(neg.f64 (/.f64 (neg.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))))))
(/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x))))
(/.f64 (neg.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) (*.f64 x (neg.f64 x)))
(/.f64 (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x) x)
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))) (neg.f64 (*.f64 x (neg.f64 x))))
(/.f64 (neg.f64 (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x)) (neg.f64 x))
(/.f64 (.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (neg.f64 (neg.f64 (neg.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))))) (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 1 binary64))) (*.f64 x (neg.f64 x)))
(pow.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x))
(.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (neg.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (*.f64 x (neg.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(approx (+ ( 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))) x) (/.f64 #s(literal 1 binary64) x))
#s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x))))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(fabs.f64 (*.f64 x (sqrt.f64 x)))
(sqrt.f64 (.f64 x (.f64 x x)))
(pow.f64 x #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/4 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(*.f64 x (sqrt.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) x)
(.f64 (.f64 x (sqrt.f64 x)) #s(literal 1 binary64))
(.f64 (.f64 x (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 3/2 binary64)) (.f64 x (sqrt.f64 x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 (*.f64 x (sqrt.f64 x))))

eval96.0ms (1.1%)

Memory: 13.6MiB live, 91.1MiB allocated
Compiler: Compiled 9 907 to 1 053 computations (89.4% saved)

prune106.0ms (1.2%)

Memory

7.7MiB live, 122.0MiB allocated

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	614	2	616
Fresh	5	2	7
Picked	2	3	5
Done	1	5	6
Total	622	12	634

Accuracy

100.0%

Counts

634 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.2%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	99.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	98.5%	(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	5.5%	(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	4.4%	(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
	3.5%	(.f64 (/.f64 (.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	98.5%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	98.7%	#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
	48.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))))

Compiler

Compiled 554 to 185 computations (66.6% saved)

regimes22.0ms (0.2%)

Memory

-13.1MiB live, 28.9MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) #s(approx (+ (* x 1/2) 1) (*.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 x))
(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 x))
(-.f64 #s(approx (/ (+ x 1) (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) #s(approx (+ x (+ x 1)) #s(literal 1 binary64)))
(-.f64 #s(approx (sqrt (+ x 1)) (sqrt.f64 x)) (sqrt.f64 x))
#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x #s(approx (+ x 1) #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x))
#s(approx (/ (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+ x (+ x 1))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1 binary64) (/.f64 x #s(approx (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 x))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (.f64 x (sqrt.f64 x)))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 #s(approx (+ (* 1/2 (sqrt (* x (* x x)))) (* (sqrt x) -1/8)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt.f64 x)) (+.f64 x (fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 1 binary64))))
(/.f64 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
#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 #s(approx (* (* (+ x (+ x 1)) (+ x (- 1 x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64) (sqrt.f64 x))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) #s(approx (/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64))) (.f64 x x))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.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))))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (.f64 (/.f64 #s(approx (+ ( -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (.f64 #s(approx ( (+ x (+ x 1)) (+ x (- 1 x))) (*.f64 x #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 x (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
(.f64 (/.f64 (.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x #s(literal -1 binary64)) x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))

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

Calls

2 calls:

13.0ms	x
7.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes12.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB allocated

Counts

20 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

-28.1MiB live, 10.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
4.4%	1	`x`
4.4%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	111
1	49	111
2	54	111
3	56	111
4	57	111

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (11.9%)

Memory

-5.8MiB live, 703.0MiB allocated

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
15 524×	`lower-fma.f64`
15 524×	`lower-fma.f32`
11 422×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	361
0	80	335
1	307	293
2	2424	285
0	8570	269
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	48	346
0	72	326
1	281	283
2	2223	275
0	8574	263
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398
0	270	3745
1	809	3283
2	2517	3238
3	6793	3222
0	8416	3031
0	254	3352
1	750	2964
2	2277	2912
3	7143	2906
0	8278	2704

Stop Event

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

Compiler

Compiled 142 to 86 computations (39.4% saved)

preprocess119.0ms (1.3%)

Memory: -3.0MiB live, 204.4MiB allocated
Compiler: Compiled 128 to 70 computations (45.3% 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

analyze2.0ms (0%)

sample1.7s (18.6%)

preprocess28.0ms (0.3%)

explain140.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.1%)

localize60.0ms (0.7%)

series5.0ms (0.1%)

simplify425.0ms (4.8%)

rewrite299.0ms (3.3%)

eval50.0ms (0.6%)

prune64.0ms (0.7%)

simplify312.0ms (3.5%)

localize144.0ms (1.6%)

series19.0ms (0.2%)

simplify427.0ms (4.8%)

rewrite372.0ms (4.2%)

eval272.0ms (3%)

prune296.0ms (3.3%)

simplify289.0ms (3.2%)

localize200.0ms (2.2%)

series15.0ms (0.2%)

simplify404.0ms (4.5%)

rewrite323.0ms (3.6%)

eval136.0ms (1.5%)

prune124.0ms (1.4%)

simplify348.0ms (3.9%)

localize219.0ms (2.4%)

series18.0ms (0.2%)

simplify533.0ms (6%)

rewrite304.0ms (3.4%)

eval96.0ms (1.1%)

prune106.0ms (1.2%)

regimes22.0ms (0.2%)

regimes12.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify7.0ms (0.1%)

soundness1.1s (11.9%)

preprocess119.0ms (1.3%)

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