Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.1s (23%)

Memory

20.8MiB live, 2 076.3MiB allocated

Samples

1.3s	6 923×	1	valid
353.0ms	1 067×	2	valid
19.0ms	266×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-div: 326.0ms (24.3% of total)

ival-sqrt: 302.0ms (22.5% of total)

const: 243.0ms (18.1% of total)

adjust: 170.0ms (12.7% of total)

ival-sub: 113.0ms (8.4% of total)

ival-add: 80.0ms (6% of total)

ival-<: 50.0ms (3.7% of total)

ival->: 34.0ms (2.5% of total)

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

exact: 7.0ms (0.5% of total)

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

Bogosity

explain149.0ms (1.6%)

Memory

8.8MiB live, 365.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
175	2	(1.173863455495768e+215)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`	cancellation	177	0

Confusion

	Predicted +	Predicted -
+	175	0
-	2	79

Precision

0.9887005649717514

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	175	0	0
-	2	0	79

Precision?

0.9887005649717514

Recall?

1.0

Freqs

test

number	freq
0	79
1	177

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

63.0ms	438×	1	valid
12.0ms	62×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 80 to 28 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-sqrt: 15.0ms (26.9% of total)

ival-div: 13.0ms (23.3% of total)

adjust: 12.0ms (21.5% of total)

ival-sub: 9.0ms (16.1% of total)

ival-add: 5.0ms (9% of total)

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

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

exact: 0.0ms (0% of total)

preprocess24.0ms (0.3%)

Memory

19.2MiB live, 57.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.9%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify16.0ms (0.2%)

Memory

-10.3MiB live, 30.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize49.0ms (0.5%)

Memory

-5.4MiB live, 108.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.265625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	39.04025041109457	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

32.0ms	219×	1	valid
6.0ms	31×	2	valid
0.0ms	6×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-sqrt: 8.0ms (30.4% of total)

ival-div: 7.0ms (26.6% of total)

adjust: 7.0ms (26.6% of total)

ival-sub: 2.0ms (7.6% of total)

ival-add: 2.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	inf	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	0	((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (/ 1 (sqrt (+ x 1))))

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify196.0ms (2.1%)

Memory

-3.3MiB live, 310.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	926	455
3	3322	445
0	8129	416

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite231.0ms (2.5%)

Memory

7.4MiB live, 244.6MiB allocated

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

4 → 238

Calls

Call 1

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

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

eval34.0ms (0.4%)

Memory: -13.9MiB live, 59.8MiB allocated
Compiler: Compiled 7 402 to 700 computations (90.5% saved)

prune146.0ms (1.6%)

Memory

-21.4MiB live, 113.5MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	272	14	286
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	14	287

Accuracy

84.5%

Counts

287 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 x x x)) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
▶	40.2%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.2%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
	39.0%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	40.2%	(/.f64 (*.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	28.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
▶	30.1%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	5.5%	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 x x x)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 x x x)))
▶	40.2%	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
	5.6%	(.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (fma.f64 x x x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (fma.f64 x x x))))
▶	83.6%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	67.1%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 520 to 296 computations (43.1% saved)

simplify118.0ms (1.3%)

Memory

26.6MiB live, 181.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

7 822×	`lower-fma.f32`
7 814×	`lower-fma.f64`
2 910×	`lower-*.f32`
2 902×	`lower-*.f64`
2 528×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	393
0	72	385
1	118	369
2	244	349
3	578	347
4	1405	347
5	4497	347
0	8341	347

Stop Event

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

Calls

Call 1

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

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

localize205.0ms (2.2%)

Memory

-7.3MiB live, 305.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	9.043507526765705	(*.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	29.772995479991767	(sqrt.f64 (fma.f64 x x x))
accuracy	29.776901729991767	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	59.81895248494932	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0.01171875	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
accuracy	0.23894501953688402	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	29.772995479991767	(sqrt.f64 (fma.f64 x x x))
accuracy	59.81895248494932	(-.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	0	#s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	39.04025041109457	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.11328125	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.47451491231524	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.4787927818796251	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)))
accuracy	0.6554880426181869	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))
accuracy	10.005226611799209	(/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))
accuracy	19.283908611253587	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)))

Samples

137.0ms	219×	1	valid
22.0ms	31×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 377 to 38 computations (89.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 114.0ms

ival-div: 49.0ms (42.9% of total)

ival-sqrt: 21.0ms (18.4% of total)

adjust: 18.0ms (15.8% of total)

ival-mult: 11.0ms (9.6% of total)

ival-add: 9.0ms (7.9% of total)

ival-sub: 7.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

series25.0ms (0.3%)

Memory

19.5MiB live, 57.2MiB allocated

Counts

20 → 240

Calls

Call 1

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

Outputs
#s(alt (sqrt (/ 1 x)) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* -1 x)) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x) (taylor 0 x) (#s(alt #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) (patch #s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (sqrt (/ 1 (pow x 7)))) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) (patch (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1/2 (* x (- (sqrt x) (* 1/4 (sqrt x))))) (* 1/2 (sqrt x))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) (patch (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) (patch (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) (patch (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 x)))) (.f64 x x)) #<representation binary64>) () ())) ())
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#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (+.f64 x #s(literal 1 binary64)) x) (patch (-.f64 (+.f64 x #s(literal 1 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -2 (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 2 (* 1/2 (/ 1 x)))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2) (taylor -inf x) (#s(alt (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (patch (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) #<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 (/ 2 x) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 (/ 1 x))) x) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/2 (* 7/8 (/ 1 x))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 7/8 (/ 1 x)))) x)) 2) x)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (patch (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1))))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) (taylor -inf x) (#s(alt (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))))) (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))) (+ (* -5/32 (sqrt -1)) (* 1/16 (sqrt -1))))))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2))))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) (taylor -inf x) (#s(alt (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (patch (.f64 (/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 3)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (patch (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x x)) (patch (sqrt.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

-inf

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (* x x)) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (- (+ x 1) x) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (+ x 1) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) (/ 1 (sqrt (+ x 1))) (sqrt (+ (* x x) x)) (sqrt (+ (* x x) -1)))

4.0ms

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (* x x)) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (- (+ x 1) x) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (+ x 1) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) (/ 1 (sqrt (+ x 1))) (sqrt (+ (* x x) x)) (sqrt (+ (* x x) -1)))

4.0ms

inf

((- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (* x x)) (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 x)) (/ 1 x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (- (+ x 1) x) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (+ x 1) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (sqrt (/ 1 (* (* x x) x))) (/ 1 (* (* x x) x)) (/ 1 (sqrt (+ x 1))) (sqrt (+ (* x x) x)) (sqrt (+ (* x x) -1)))

simplify224.0ms (2.4%)

Memory

10.5MiB live, 252.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 322×	`lower-fma.f64`
12 322×	`lower-fma.f32`
5 290×	`lower-*.f64`
5 290×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	484	3715
1	1489	3124
2	5044	3063
0	8789	2890

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 236

Calls

Call 1

Inputs
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* 1/2 (sqrt (/ 1 (pow x 7))))
(/ (+ (* -1/2 (* x (- (sqrt x) (* 1/4 (sqrt x))))) (* 1/2 (sqrt x))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (* x (- (sqrt x) (* 1/4 (sqrt x))))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 2))
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (- (* x (- (sqrt x) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(/ (- (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(/ (- (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
1
1
1
1
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1 (sqrt -1)) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* (sqrt -1) (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (* 1/2 (/ 1 (* x (sqrt -1))))))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* x (- (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 (pow x 5))))) (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* x (- (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 (pow x 5))))) (+ (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 (pow x 3)))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
1
1
1
1
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 13/128 (/ 1 (pow x 3))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/2 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (- (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (- (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* -1/4 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* (sqrt (/ 1 x)) (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)
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
1
1
1
1
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(/ 2 x)
(/ (+ 2 (* 1/2 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 7/8 (/ 1 x))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 7/8 (/ 1 x)))) x)) 2) x))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1))))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))))) (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))) (+ (* -5/32 (sqrt -1)) (* 1/16 (sqrt -1))))))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2))))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))

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

rewrite183.0ms (2%)

Memory

-23.6MiB live, 204.9MiB allocated

Rules

4 694×	`lower-*.f32`
4 686×	`lower-*.f64`
4 254×	`lower-/.f32`
4 240×	`lower-/.f64`
2 766×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	267
0	72	255
1	294	227
2	2509	221
0	8950	216

Stop Event

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

Counts

20 → 754

Calls

Call 1

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

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

eval515.0ms (5.6%)

Memory: -191.6MiB live, 286.8MiB allocated
Compiler: Compiled 46 258 to 4 351 computations (90.6% saved)

prune192.0ms (2.1%)

Memory

15.1MiB live, 404.8MiB allocated

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1 538	18	1 556
Fresh	8	1	9
Picked	3	2	5
Done	0	0	0
Total	1 549	21	1 570

Accuracy

100.0%

Counts

1 570 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.5%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.2%	(/.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
▶	84.3%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	40.2%	(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	39.0%	(/.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	40.2%	(/.f64 (.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) (.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)))
	98.2%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	25.4%	(-.f64 #s(approx (/ 1 (sqrt x)) (/.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	30.1%	(-.f64 #s(approx (/ 1 (sqrt x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	40.2%	(*.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
▶	83.5%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
▶	82.9%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
	98.2%	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
	67.1%	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))
	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	98.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) x))) x) (/.f64 #s(literal -1/2 binary64) x)))
	38.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	22.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) #s(approx (/ (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (* x x)) (/.f64 (fma.f64 (fma.f64 (sqrt.f64 (.f64 (.f64 x x) x)) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 3/4 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64))) x (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 (.f64 x x) (.f64 x x)))))

Compiler

Compiled 627 to 368 computations (41.3% saved)

simplify129.0ms (1.4%)

Memory

-10.6MiB live, 165.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 (sqrt.f64 (fma.f64 x x x)) x)
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
cost-diff	384	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
cost-diff	0	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x))
cost-diff	0	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x)))
cost-diff	0	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
cost-diff	0	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
cost-diff	0	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
cost-diff	0	(-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x)))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) x))) x) (/.f64 #s(literal -1/2 binary64) x)))
cost-diff	64	(/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x))) x)
cost-diff	1280	(.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) x))) x) (/.f64 #s(literal -1/2 binary64) x))

Rules

8 044×	`lower-fma.f32`
8 040×	`lower-fma.f64`
2 926×	`lower-*.f32`
2 916×	`lower-*.f64`
2 744×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	387
0	83	387
1	133	387
2	235	359
3	448	359
4	983	359
5	3227	355
6	6588	353
0	8056	349

Stop Event

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

Calls

Call 1

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

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

localize237.0ms (2.6%)

Memory

17.4MiB live, 284.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (sqrt.f64 (fma.f64 x x x)) x)
accuracy	0.01171875	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
accuracy	0.23894501953688402	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	29.772995479991767	(sqrt.f64 (fma.f64 x x x))
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.4965539810615258	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x)))
accuracy	0.8780693049935379	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x))
accuracy	9.043507526765705	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.8819755549935379	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
accuracy	0.9411897186137301	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
accuracy	9.043507526765705	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	0	(sqrt.f64 x)
accuracy	0.265625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.47451491231524	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.23046875	(.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) x))) x) (/.f64 #s(literal -1/2 binary64) x))
accuracy	0.4787927818796251	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x)) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 x) x))) x) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	0.5078125	(/.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
accuracy	21.697853197742063	(/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) (*.f64 (sqrt.f64 x) x))

Samples

123.0ms	219×	1	valid
48.0ms	31×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 337 to 42 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-div: 57.0ms (42.6% of total)

ival-sqrt: 29.0ms (21.7% of total)

adjust: 19.0ms (14.2% of total)

ival-mult: 11.0ms (8.2% of total)

ival-sub: 10.0ms (7.5% of total)

ival-add: 7.0ms (5.2% of total)

exact: 1.0ms (0.7% of total)

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

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

series49.0ms (0.5%)

Memory

-14.0MiB live, 29.5MiB allocated

Counts

23 → 276

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

inf

((* (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (/ -1/2 x)) (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ 1/2 (* x x)) (* x x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ (- 1/2 (/ 1/8 x)) (* x x)) (- 1/2 (/ 1/8 x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x) (/ (+ (* 1/4 x) 1) (* (sqrt x) x)) (/ (- 1 x) (sqrt x)) (sqrt (- x 1)) (sqrt (+ (* x x) x)))

4.0ms

-inf

((* (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (/ -1/2 x)) (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ 1/2 (* x x)) (* x x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ (- 1/2 (/ 1/8 x)) (* x x)) (- 1/2 (/ 1/8 x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x) (/ (+ (* 1/4 x) 1) (* (sqrt x) x)) (/ (- 1 x) (sqrt x)) (sqrt (- x 1)) (sqrt (+ (* x x) x)))

3.0ms

((* (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (/ -1/2 x)) (/ (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) x) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ (- 1 x) (sqrt x)) (/ (+ (* 1/4 x) 1) (* (sqrt x) x))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt x)) (sqrt x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ 1/2 (* x x)) (* x x) (* (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (sqrt (- x 1))) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/ (- 1/2 (/ 1/8 x)) (* x x)) (- 1/2 (/ 1/8 x)) (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x) (/ (+ (* 1/4 x) 1) (* (sqrt x) x)) (/ (- 1 x) (sqrt x)) (sqrt (- x 1)) (sqrt (+ (* x x) x)))

simplify191.0ms (2.1%)

Memory

30.1MiB live, 184.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 284×	`lower-fma.f64`
13 284×	`lower-fma.f32`
5 024×	`lower-*.f64`
5 024×	`lower-*.f32`
3 856×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	4292
1	1523	3681
2	5036	3577
0	8735	3385

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 275

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 (pow x 7))))
(/ (+ (* -1/2 (* x (- (sqrt x) (* 1/4 (sqrt x))))) (* 1/2 (sqrt x))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4))
(/ (+ (* 1/2 (sqrt x)) (* x (+ (* -1/2 (- (sqrt x) (* 1/4 (sqrt x)))) (* 1/2 (sqrt (pow x 3)))))) (pow x 4))
(* -1 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1 (sqrt x)) (* x (- (sqrt x) (* 1/4 (sqrt x))))) (pow x 3))
(/ (+ (* -1 (sqrt x)) (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x))))) (pow x 3))
(/ (+ (* -1 (sqrt x)) (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x))))) (pow x 3))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(* -1 (sqrt (/ 1 (pow x 3))))
(/ (- (* x (- (sqrt x) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(/ (- (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(/ (- (* x (- (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (* 1/4 (sqrt x)))) (sqrt x)) (pow x 2))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1 (sqrt -1)) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* (sqrt -1) (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (* 1/2 (/ 1 (* x (sqrt -1))))))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
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(/ (- (* 1/2 x) 1/8) (pow x 3))
(/ (- (* 1/2 x) 1/8) (pow x 3))
(/ -1/8 x)
(/ (- (* 1/2 x) 1/8) x)
(/ (- (* 1/2 x) 1/8) x)
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(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
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1
1
1
1
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(+ x (sqrt x))
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(sqrt (/ 1 (pow x 3)))
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(/ (+ (sqrt x) (* 1/4 (sqrt (pow x 3)))) (pow x 2))
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(sqrt x)
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(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(/ (+ (* -1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)) (+ (* 1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt (/ 1 (pow x 5)))))) x)
(* -1 (sqrt (/ 1 x)))
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(- (+ (sqrt (/ 1 (pow x 3))) (+ (* -1 (sqrt (/ 1 x))) (* -1 (sqrt (/ 1 (pow x 5)))))) (* 1/4 (sqrt (/ 1 (pow x 3)))))
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(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
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(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
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(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 (pow x 2))
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(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 13/128 (/ 1 (pow x 3))))) (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
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(pow x 2)
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(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 13/128 (/ 1 (pow x 3))))) (pow x 2))
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
1
1
1
1
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 1/4 (sqrt (/ 1 x)))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(* x (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x))))) (* 1/2 (sqrt (/ 1 (pow x 3))))) x)) (* -1/2 (sqrt (/ 1 x)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x))))) (* 1/2 (sqrt (/ 1 (pow x 3))))) x)) (* -1/2 (sqrt (/ 1 x)))) x))
(* -1 (sqrt (/ 1 x)))
(- (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))
(+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))))) x)))
(+ (* -1 (sqrt (/ 1 x))) (* -1 (/ (+ (sqrt (/ 1 (pow x 3))) (* -1 (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))))) x)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (sqrt x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (- (sqrt (/ 1 x)) (* 1/4 (sqrt (/ 1 x)))) x)))))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (- (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3))))) (* 1/4 (sqrt (/ 1 x)))) x)))))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (/ (- (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3))))) (* 1/4 (sqrt (/ 1 x)))) x)))))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1))))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))))) (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))) (+ (* -5/32 (sqrt -1)) (* 1/16 (sqrt -1))))))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2))))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(/ 2 x)
(/ (+ 2 (* 1/2 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 7/8 (/ 1 x))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 7/8 (/ 1 x)))) x)) 2) x))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1))))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))))) (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))) (+ (* -5/32 (sqrt -1)) (* 1/16 (sqrt -1))))))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2))))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(/ 2 x)
(/ (+ 2 (* 1/2 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 7/8 (/ 1 x))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 7/8 (/ 1 x)))) x)) 2) x))
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
1
1
1
1
-1/2
(- (* 1/8 (/ 1 x)) 1/2)
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2)
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2)
(* 1/4 (sqrt (/ 1 x)))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* 1/4 (sqrt (/ 1 x))))
(* -1 (sqrt x))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (sqrt (/ 1 x)) (* -1 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))

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

rewrite400.0ms (4.4%)

Memory

2.9MiB live, 226.8MiB allocated

Rules

5 334×	`lower-/.f32`
5 314×	`lower-/.f64`
2 744×	`lower-*.f32`
2 734×	`lower-*.f64`
2 306×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	329
0	83	329
1	339	318
2	3026	310
0	8501	298

Stop Event

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

Counts

23 → 700

Calls

Call 1

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

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

eval535.0ms (5.8%)

Memory: 4.3MiB live, 239.4MiB allocated
Compiler: Compiled 28 043 to 3 184 computations (88.6% saved)

prune450.0ms (4.9%)

Memory

13.3MiB live, 253.8MiB allocated

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	1 088	11	1 099
Fresh	8	6	14
Picked	2	3	5
Done	1	1	2
Total	1 099	21	1 120

Accuracy

100.0%

Counts

1 120 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	84.3%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	99.0%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	84.3%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
▶	99.4%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	98.2%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	84.3%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)))
	40.2%	(*.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
	67.7%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal -1/8 binary64)) (.f64 (.f64 x x) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
▶	84.4%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
✓	82.9%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
	82.8%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(approx (sqrt (- x 1)) (sqrt.f64 x)))
	98.2%	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x))
	67.1%	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))
▶	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	97.2%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 x (/.f64 (-.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 (fma.f64 #s(literal 1/4 binary64) x #s(literal 1 binary64)) x)) (sqrt.f64 x))) x)))
	98.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (- (/ (- 1 x) (sqrt x)) (/ (+ ( 1/4 x) 1) (* (sqrt x) x))) (neg.f64 (sqrt.f64 x))) x) (/.f64 #s(literal -1/2 binary64) x)))
	98.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (/ (- (/ (- 1 x) (sqrt x)) (/ (+ ( 1/4 x) 1) (* (sqrt x) x))) x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1/2 binary64) x)))
	38.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 528 to 323 computations (38.8% saved)

simplify286.0ms (3.1%)

Memory

-27.9MiB live, 105.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	384	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))
cost-diff	0	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
cost-diff	384	(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(/.f64 (sqrt.f64 x) x)
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
cost-diff	0	#s(approx (- (+ x 1) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))))
cost-diff	384	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	448	(.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))

Rules

10 388×	`lower-fma.f32`
10 386×	`lower-fma.f64`
2 452×	`lower-*.f32`
2 446×	`lower-*.f64`
2 192×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	346
0	71	346
1	104	346
2	168	306
3	308	306
4	475	296
5	1047	296
6	2317	296
7	4878	296
8	7137	296
0	8332	289

Stop Event

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

Calls

Call 1

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

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

localize245.0ms (2.7%)

Memory

11.4MiB live, 169.8MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (sqrt.f64 (fma.f64 x x x)) x)
accuracy	0.1875	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
accuracy	0.2578125	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	29.772995479991767	(sqrt.f64 (fma.f64 x x x))
accuracy	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.109375	(/.f64 (/.f64 #s(literal 1/2 binary64) x) x)
accuracy	0.9411897186137301	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x))
accuracy	9.043507526765705	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.23894501953688402	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.9423006973751444	#s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.24609375	(/.f64 (sqrt.f64 x) x)
accuracy	60.47451491231524	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
accuracy	0.01171875	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))))
accuracy	0.18362480091517802	#s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
accuracy	0.23894501953688402	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) #s(approx (+ (sqrt (+ (* x x) x)) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.835100555027012	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

Samples

197.0ms	219×	1	valid
17.0ms	31×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 286 to 36 computations (87.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-div: 27.0ms (31.4% of total)

adjust: 16.0ms (18.6% of total)

ival-sub: 16.0ms (18.6% of total)

ival-sqrt: 12.0ms (14% of total)

ival-add: 8.0ms (9.3% of total)

ival-mult: 6.0ms (7% 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

-3.8MiB live, 34.1MiB allocated

Counts

22 → 264

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

5.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify165.0ms (1.8%)

Memory

-11.9MiB live, 179.6MiB allocated

Algorithm

1×	egg-herbie

Rules

13 808×	`lower-fma.f64`
13 808×	`lower-fma.f32`
4 628×	`lower-*.f64`
4 628×	`lower-*.f32`
3 680×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	488	3778
1	1517	3241
2	5131	3151
0	8540	2965

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 261

Calls

Call 1

Inputs
(/ -1/8 x)
(/ (- (* 2 (pow x 2)) 1/8) x)
(/ (- (* 2 (pow x 2)) 1/8) x)
(/ (- (* 2 (pow x 2)) 1/8) x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
1
1
1
1
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 x)) x)
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(sqrt (/ 1 x))
(- (sqrt (/ 1 x)) 1)
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (/ 1 x))))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* (sqrt (/ 1 x)) (sqrt -1))
(+ (* -1 (sqrt -1)) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* x (+ (* -1 (/ (sqrt -1) x)) (* x (+ (* -1 (* (sqrt -1) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* (sqrt -1) (- (* 1/2 (/ 1 (pow x 2))) (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))) (* 1/2 (/ 1 (* x (sqrt -1))))))))))) (* (sqrt (/ 1 x)) (sqrt -1)))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(sqrt x)
(+ x (sqrt x))
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(sqrt x)
(+ x (sqrt x))
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))
(* 2 x)
(* x (- 2 (* 1/8 (/ 1 (pow x 2)))))
(* x (- 2 (* 1/8 (/ 1 (pow x 2)))))
(* x (- 2 (* 1/8 (/ 1 (pow x 2)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
1
1
1
1
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(/ (- (* 1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))) (pow x 2))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 5/128 (/ 1 (pow x 3))))) x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(/ 1/2 (pow x 2))
(/ (- 1/2 (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (* 1/8 (/ 1 x))) (pow x 2))
(/ (- (+ 1/2 (/ 5/16 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 13/128 (/ 1 (pow x 3))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 5))))))
(+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 (pow x 5)))))))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 2 x)
(* -1 (* x (- (* 1/8 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ 1 (pow x 2))) 2)))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
1
1
1
1
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 5))))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
-2
(* -1 (+ 2 (* 1/2 (/ 1 x))))
(- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)
(- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1))))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))))) (* -1 (/ (+ (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ (* -1/4 (+ (* -1/4 (sqrt -1)) (* 1/8 (sqrt -1)))) (+ (* -5/32 (sqrt -1)) (* 1/16 (sqrt -1))))))) (* 1/4 (* (sqrt x) (pow (sqrt -1) 2))))) x)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(/ 2 x)
(/ (+ 2 (* 1/2 (/ 1 x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/2 (* 7/8 (/ 1 x))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (+ 1/2 (+ (/ 5/16 (pow x 2)) (* 7/8 (/ 1 x)))) x)) 2) x))
(* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (sqrt x) (+ (* -1 (/ (+ (sqrt x) (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) x)) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
-1/2
(- (* 1/8 (/ 1 x)) 1/2)
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2)
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x)))))
(* -1 (* x (+ 1 (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x)))))
-1/2
(- (* 1/8 (/ 1 x)) 1/2)
(- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2)
(- (* -1 (/ (- (* -1 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2)

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

rewrite188.0ms (2%)

Memory

0.2MiB live, 281.5MiB allocated

Rules

4 722×	`lower-/.f32`
4 704×	`lower-/.f64`
4 634×	`lower-*.f32`
4 628×	`lower-*.f64`
3 132×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	280
0	71	280
1	286	278
2	2235	276
0	8739	257

Stop Event

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

Counts

22 → 484

Calls

Call 1

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

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

eval136.0ms (1.5%)

Memory: 6.7MiB live, 277.9MiB allocated
Compiler: Compiled 19 307 to 2 078 computations (89.2% saved)

prune164.0ms (1.8%)

Memory

-1.3MiB live, 325.9MiB allocated

Pruning

24 alts after pruning (16 fresh and 8 done)

	Pruned	Kept	Total
New	977	8	985
Fresh	4	8	12
Picked	1	4	5
Done	0	4	4
Total	982	24	1 006

Accuracy

100.0%

Counts

1 006 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	84.3%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	99.0%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (+.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	84.3%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x x)) x))
	99.0%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x)) x))
	98.2%	(/.f64 (/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #s(approx (+ (sqrt (+ (* x x) x)) x) (*.f64 #s(literal 2 binary64) x)))
✓	98.2%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	38.8%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
	98.0%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ x 1)) (.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))
	98.1%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ x 1)) (sqrt.f64 x)))
	7.8%	(/.f64 #s(approx (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (/.f64 #s(literal 1/2 binary64) x)) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
	84.3%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (*.f64 (+.f64 (sqrt.f64 (fma.f64 x x x)) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	97.6%	(/.f64 #s(approx (- (+ x 1) x) #s(literal 1 binary64)) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(approx (+ (sqrt (+ ( x x) x)) x) (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)) #s(literal 2 binary64)) x #s(literal 1/2 binary64)))))
	40.2%	(*.f64 (/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) x) (+.f64 (sqrt.f64 (fma.f64 x x x)) x)) (sqrt.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
✓	84.4%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
✓	82.9%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
	82.8%	(.f64 #s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ ( x x) x)) x)) (sqrt (+ (* x x) -1))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(approx (sqrt (- x 1)) (sqrt.f64 x)))
	67.1%	#s(approx (/ (/ (- (+ x 1) x) (+ (sqrt (+ (* x x) x)) x)) (sqrt (+ x 1))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) #s(literal 1/2 binary64)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (sqrt.f64 x) x))
	82.8%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(approx (* -1/2 (- (sqrt (/ 1 x)) (+ (* (+ (* 1/4 x) 1) (sqrt (/ 1 (* (* x x) x)))) (sqrt x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (.f64 x x)))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	98.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (- (/ (- 1 x) (sqrt x)) (/ (+ ( 1/4 x) 1) (* (sqrt x) x))) (neg.f64 (sqrt.f64 x))) x) (/.f64 #s(literal -1/2 binary64) x)))
	98.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(approx (/ (- (/ (- 1 x) (sqrt x)) (/ (+ ( 1/4 x) 1) (* (sqrt x) x))) x) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1/2 binary64) x)))
	38.0%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 x (*.f64 x x))))
✓	5.5%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 1 103 to 345 computations (68.7% saved)

regimes52.0ms (0.6%)

Memory

6.5MiB live, 44.4MiB allocated

Counts

52 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

39.0ms	x
11.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes19.0ms (0.2%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

36 → 1

Calls

Call 1

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

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

Calls

2 calls:

10.0ms	x
8.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes22.0ms (0.2%)

Memory

-17.1MiB live, 21.4MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

2 calls:

15.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
5.0ms	x

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes7.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes10.0ms (0.1%)

Memory

-28.4MiB live, 11.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs

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

Calls

2 calls:

7.0ms	x
2.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
82.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
82.8%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
38.8%	1	`x`
38.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
38.0%	1	`x`
38.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes4.0ms (0%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
7.8%	1	`x`
7.8%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes5.0ms (0.1%)

Memory

-30.4MiB live, 8.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

3.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
5.5%	1	`x`
5.5%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify8.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
12×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	239
1	78	239
2	86	239
3	95	239
4	102	239
5	106	239
6	107	239

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (14.5%)

Memory

20.1MiB live, 876.1MiB allocated

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
13 808×	`lower-fma.f64`
13 808×	`lower-fma.f32`
13 284×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	114	529
1	303	480
2	926	455
3	3322	445
0	8129	416
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	497	4292
1	1523	3681
2	5036	3577
0	8735	3385
0	484	3715
1	1489	3124
2	5044	3063
0	8789	2890
0	54	329
0	83	329
1	339	318
2	3026	310
0	8501	298
0	42	267
0	72	255
1	294	227
2	2509	221
0	8950	216
0	488	3778
1	1517	3241
2	5131	3151
0	8540	2965

Stop Event

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

Compiler

Compiled 264 to 140 computations (47% saved)

preprocess88.0ms (1%)

Memory: 0.5MiB live, 155.3MiB allocated
Compiler: Compiled 258 to 110 computations (57.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

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

start0.0ms (0%)

analyze2.0ms (0%)

sample2.1s (23%)

explain149.0ms (1.6%)

preprocess24.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify16.0ms (0.2%)

localize49.0ms (0.5%)

series6.0ms (0.1%)

simplify196.0ms (2.1%)

rewrite231.0ms (2.5%)

eval34.0ms (0.4%)

prune146.0ms (1.6%)

simplify118.0ms (1.3%)

localize205.0ms (2.2%)

series25.0ms (0.3%)

simplify224.0ms (2.4%)

rewrite183.0ms (2%)

eval515.0ms (5.6%)

prune192.0ms (2.1%)

simplify129.0ms (1.4%)

localize237.0ms (2.6%)

series49.0ms (0.5%)

simplify191.0ms (2.1%)

rewrite400.0ms (4.4%)

eval535.0ms (5.8%)

prune450.0ms (4.9%)

simplify286.0ms (3.1%)

localize245.0ms (2.7%)

series19.0ms (0.2%)

simplify165.0ms (1.8%)

rewrite188.0ms (2%)

eval136.0ms (1.5%)

prune164.0ms (1.8%)

regimes52.0ms (0.6%)

regimes19.0ms (0.2%)

regimes22.0ms (0.2%)

regimes7.0ms (0.1%)

regimes10.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes5.0ms (0.1%)

simplify8.0ms (0.1%)

soundness1.3s (14.5%)

preprocess88.0ms (1%)

end0.0ms (0%)

Profiling

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

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