Metrics for 2isqrt (example 3.6)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.0s (21.2%)

Memory

34.7MiB live, 2 086.9MiB allocated

Samples

1.2s	6 886×	1	valid
287.0ms	1 103×	2	valid
40.0ms	267×	0	valid

Precisions

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

ival-sqrt: 332.0ms (26.4% of total)

ival-div: 330.0ms (26.3% of total)

adjust: 178.0ms (14.2% of total)

const: 125.0ms (10% of total)

ival-add: 104.0ms (8.3% of total)

ival-sub: 77.0ms (6.1% of total)

ival->: 68.0ms (5.4% of total)

ival-<: 21.0ms (1.7% of total)

ival-and: 11.0ms (0.9% of total)

exact: 7.0ms (0.6% of total)

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

Bogosity

explain166.0ms (1.8%)

Memory

-22.7MiB live, 234.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
167	1	(3.177700596478893e+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	168	0

Confusion

	Predicted +	Predicted -
+	167	0
-	1	88

Precision

0.9940476190476191

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	167	0	0
-	1	0	88

Precision?

0.9940476190476191

Recall?

1.0

Freqs

test

number	freq
0	88
1	168

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

67.0ms	426×	1	valid
15.0ms	74×	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: 62.0ms

ival-sqrt: 21.0ms (34.1% of total)

ival-div: 20.0ms (32.5% of total)

adjust: 9.0ms (14.6% of total)

ival-add: 5.0ms (8.1% of total)

ival-sub: 5.0ms (8.1% of total)

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

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

exact: 0.0ms (0% of total)

preprocess26.0ms (0.3%)

Memory

6.3MiB live, 44.0MiB 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 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	42.5%	(-.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)

simplify15.0ms (0.2%)

Memory

-20.6MiB live, 16.7MiB 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 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)

localize50.0ms (0.5%)

Memory

23.0MiB live, 68.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	0.29296875	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	36.774997693785	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

31.0ms	213×	1	valid
7.0ms	37×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-sqrt: 8.0ms (32% of total)

ival-div: 7.0ms (28% of total)

adjust: 5.0ms (20% of total)

ival-add: 2.0ms (8% of total)

ival-sub: 2.0ms (8% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

-30.6MiB live, 8.4MiB 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 (* 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)) (* (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 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 (/ 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 (/ 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 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#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 (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)) (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

12 calls:

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

simplify288.0ms (3%)

Memory

25.0MiB live, 459.2MiB 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	925	455
3	3326	445
0	8140	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)
(* 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)) (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))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
1
(+ 1 (* -1/2 x))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(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)) (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) #s(literal -1 binary64))
(/ (+ (sqrt x) (* x (- (* 1/2 x) 1))) x)
(/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64)) (sqrt.f64 x)) x)
(/ (+ (sqrt x) (* x (- (* x (+ 1/2 (* -3/8 x))) 1))) x)
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal -3/8 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (sqrt.f64 x)) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (- (* -1/2 (sqrt (/ 1 x))) (* -1/2 (sqrt x))) (pow x 2))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x 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 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(- (+ (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 -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 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(- (+ (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 1/2 binary64) (+.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))) (sqrt.f64 x)) (.f64 x (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 3/8 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal -5/16 binary64) #s(literal 3/8 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(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 x (.f64 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) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 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 #s(literal -1/2 binary64) (fma.f64 (fma.f64 x #s(literal 1/4 binary64) #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 x (.f64 x x))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(+ (* -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 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64))) (sqrt.f64 x)) (.f64 x (.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

rewrite239.0ms (2.5%)

Memory

3.0MiB live, 356.9MiB 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 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(+.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (neg.f64 (sqrt.f64 (/.f64 x (fma.f64 x x x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (sqrt.f64 (/.f64 x (fma.f64 x x x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x))))
(-.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x x))) (neg.f64 (sqrt.f64 (/.f64 x (fma.f64 x x x)))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 x (sqrt.f64 x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x))) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 x x x))) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) x)) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) x)))))
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(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 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)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (log1p.f64 x) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) (.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 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 x #s(literal -1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))

eval37.0ms (0.4%)

Memory: 0.9MiB live, 73.4MiB allocated
Compiler: Compiled 7 402 to 706 computations (90.5% saved)

prune59.0ms (0.6%)

Memory

-6.4MiB live, 120.2MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	275	11	286
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	11	287

Accuracy

82.2%

Counts

287 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.2%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	44.2%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
▶	42.5%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
	44.2%	(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	30.5%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
	33.2%	(-.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)))))
	44.2%	(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	81.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
	80.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
	65.7%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
▶	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 362 to 212 computations (41.4% saved)

simplify218.0ms (2.3%)

Memory

36.0MiB live, 230.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

10 320×	`lower-fma.f32`
10 314×	`lower-fma.f64`
3 388×	`lower-*.f32`
3 382×	`lower-*.f64`
1 878×	`lower-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	329
0	63	309
1	114	301
2	226	301
3	443	301
4	1046	301
5	2369	301
6	5369	301
0	8157	301

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

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

localize257.0ms (2.7%)

Memory

-18.6MiB live, 354.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.21322250976844204	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	33.26970387161623	(sqrt.f64 (fma.f64 x x x))
accuracy	59.33458849721694	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 x)
accuracy	0.18359375	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
accuracy	33.26970387161623	(sqrt.f64 (fma.f64 x x x))
accuracy	59.94558538171301	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.1171875	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	1.0969491818279222	#s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	36.774997693785	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(approx (/ 1 (sqrt (+ x 1))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0.1171875	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	60.520678386379345	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
accuracy	0.464559553181604	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	0.4896382610434905	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
accuracy	11.520255549175625	(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x))
accuracy	20.353344935321648	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Samples

129.0ms	213×	1	valid
22.0ms	37×	2	valid
3.0ms	6×	0	valid

Compiler

Compiled 306 to 35 computations (88.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-div: 33.0ms (30% of total)

adjust: 26.0ms (23.7% of total)

ival-sqrt: 17.0ms (15.5% of total)

ival-add: 12.0ms (10.9% of total)

ival-mult: 12.0ms (10.9% of total)

ival-sub: 9.0ms (8.2% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.2%)

Memory

-5.1MiB live, 34.1MiB allocated

Counts

21 → 252

Calls

Call 1

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

63 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x)))
1.0ms	x	@	-inf	(/ (- (sqrt (+ 1 x)) (sqrt x)) (sqrt (+ (* x x) x)))
1.0ms	x	@	0	(/ (* 1/2 (- (+ (* (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x)))) (* x x))
1.0ms	x	@	0	(/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x)))
1.0ms	x	@	-inf	(- (sqrt (+ 1 x)) (sqrt x))

simplify282.0ms (3%)

Memory

7.2MiB live, 388.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 698×	`lower-fma.f64`
16 698×	`lower-fma.f32`
5 182×	`lower-*.f64`
5 182×	`lower-*.f32`
5 074×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	490	3730
1	1465	3220
2	4803	3185
0	8736	2997

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 249

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

rewrite286.0ms (3%)

Memory

11.0MiB live, 330.1MiB allocated

Rules

5 422×	`lower-*.f32`
5 416×	`lower-*.f64`
3 468×	`lower-/.f32`
3 454×	`lower-/.f64`
2 790×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	245
0	63	233
1	302	188
2	2636	183
0	8750	180

Stop Event

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

Counts

21 → 771

Calls

Call 1

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

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

eval337.0ms (3.6%)

Memory: -133.6MiB live, 277.4MiB allocated
Compiler: Compiled 39 245 to 4 108 computations (89.5% saved)

prune210.0ms (2.2%)

Memory

-19.9MiB live, 346.7MiB allocated

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	1 528	13	1 541
Fresh	6	0	6
Picked	4	1	5
Done	0	0	0
Total	1 538	14	1 552

Accuracy

100.0%

Counts

1 552 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.5%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	82.0%	(/.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	82.0%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
	42.1%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
	98.0%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	80.4%	(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
▶	82.0%	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
▶	82.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
	98.0%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x))
▶	65.7%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	80.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
▶	5.4%	#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 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 388 to 242 computations (37.6% saved)

simplify203.0ms (2.1%)

Memory

22.4MiB live, 171.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
cost-diff	0	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
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 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x)))
cost-diff	0	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	64	(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x)
cost-diff	1664	(.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x))

Rules

7 684×	`lower-fma.f32`
7 680×	`lower-fma.f64`
2 544×	`lower-*.f32`
2 530×	`lower-*.f64`
1 586×	`lower-/.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	49	321
0	76	311
1	124	307
2	178	307
3	225	307
4	306	307
5	581	301
6	1184	301
7	3122	301
8	5645	301
0	8470	301

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

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

localize269.0ms (2.8%)

Memory

2.7MiB live, 313.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.15234375	(*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x)))
accuracy	0.9938845425782031	(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
accuracy	33.26970387161623	(sqrt.f64 (fma.f64 x x x))
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.1484375	(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x))))
accuracy	0.9938845425782031	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
accuracy	33.26970387161623	(sqrt.f64 (fma.f64 x x x))
accuracy	0.078125	(.f64 x (.f64 x x))
accuracy	0.464559553181604	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
accuracy	1.1229297631790216	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
accuracy	20.353344935321648	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
accuracy	0	(sqrt.f64 x)
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	60.520678386379345	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
accuracy	0.22265625	(/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x)
accuracy	0.4896382610434905	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.5234375	(/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))
accuracy	23.34523559454242	(/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x (sqrt.f64 x)))

Samples

152.0ms	213×	1	valid
32.0ms	37×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 299 to 41 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-div: 69.0ms (45.8% of total)

ival-add: 23.0ms (15.3% of total)

adjust: 19.0ms (12.6% of total)

ival-sqrt: 17.0ms (11.3% of total)

ival-mult: 17.0ms (11.3% of total)

ival-sub: 4.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series29.0ms (0.3%)

Memory

-18.5MiB live, 34.3MiB allocated

Counts

22 → 264

Calls

Call 1

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

66 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(/ (+ x -1) (sqrt x))
2.0ms	x	@	-inf	(* 1/2 (sqrt (/ 1 (* x (* x x)))))
2.0ms	x	@	-inf	(* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) x) (/ 1/2 x))
1.0ms	x	@	0	(/ 1 (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))))
1.0ms	x	@	0	(* (/ (+ (/ (+ (* x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) x) (/ 1/2 x))

simplify306.0ms (3.2%)

Memory

42.4MiB live, 353.2MiB allocated

Algorithm

1×	egg-herbie

Rules

12 522×	`lower-fma.f64`
12 522×	`lower-fma.f32`
5 218×	`lower-*.f64`
5 218×	`lower-*.f32`
4 132×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	562	4315
1	1784	3789
2	6200	3779
0	8123	3550

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 261

Calls

Call 1

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

rewrite336.0ms (3.5%)

Memory

-4.5MiB live, 521.9MiB allocated

Rules

5 848×	`lower-/.f32`
5 832×	`lower-/.f64`
4 226×	`lower-fma.f32`
4 222×	`lower-fma.f64`
4 076×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	259
0	76	249
1	322	214
2	2876	213
0	9344	205

Stop Event

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

Counts

22 → 1 100

Calls

Call 1

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

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

eval310.0ms (3.3%)

Memory: -36.9MiB live, 405.4MiB allocated
Compiler: Compiled 41 059 to 5 137 computations (87.5% saved)

prune593.0ms (6.3%)

Memory

27.9MiB live, 417.8MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	1 654	8	1 662
Fresh	3	5	8
Picked	2	3	5
Done	0	1	1
Total	1 659	17	1 676

Accuracy

100.0%

Counts

1 676 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	43.5%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	82.0%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
	42.1%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
	98.0%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	67.4%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x x)))))
	97.6%	(/.f64 #s(literal 1 binary64) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x))))
✓	82.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	97.7%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
▶	7.7%	(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
	96.6%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
▶	98.2%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))))
▶	97.9%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
✓	65.7%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	80.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
✓	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	97.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 357 to 221 computations (38.1% saved)

simplify189.0ms (2%)

Memory

4.7MiB live, 165.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

9 246×	`lower-fma.f64`
9 246×	`lower-fma.f32`
2 380×	`lower-*.f32`
2 374×	`lower-*.f64`
1 290×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	287
0	61	279
1	106	263
2	167	263
3	213	263
4	274	263
5	502	263
6	1080	263
7	3810	263
8	6906	263
0	8071	251

Stop Event

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

Calls

Call 1

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

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

localize235.0ms (2.5%)

Memory

-30.5MiB live, 137.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.21322250976844204	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.4569057019600189	#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))
accuracy	59.33458849721694	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0.00390625	(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
accuracy	0.18359375	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
accuracy	1.1229297631790216	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.1484375	(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x))))
accuracy	0.4569057019600189	#s(approx (sqrt (+ (* x x) x)) (+.f64 #s(literal 1/2 binary64) x))
accuracy	0.9938845425782031	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
accuracy	0	(+.f64 x (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.9938845425782031	(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
accuracy	59.06333301379064	#s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))
accuracy	0	(pow.f64 x #s(literal -3/2 binary64))
accuracy	0.00390625	(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
accuracy	1.1229297631790216	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))))

Samples

162.0ms	233×	1	valid
5.0ms	23×	0	valid

Compiler

Compiled 232 to 29 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 23.0ms (30.1% of total)

ival-div: 14.0ms (18.3% of total)

adjust: 13.0ms (17% of total)

ival-add: 11.0ms (14.4% of total)

ival-sqrt: 7.0ms (9.2% of total)

ival-pow: 7.0ms (9.2% of total)

ival-sub: 2.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

20 → 240

Calls

Call 1

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

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

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(pow x -3/2)
1.0ms	x	@	0	(pow x -3/2)
0.0ms	x	@	-inf	(/ (/ 1 (sqrt x)) x)
0.0ms	x	@	inf	(pow x -3/2)
0.0ms	x	@	-inf	(* 1/2 (/ (/ 1 (sqrt x)) x))

simplify359.0ms (3.8%)

Memory

-2.7MiB live, 273.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 166×	`lower-fma.f64`
13 166×	`lower-fma.f32`
4 488×	`lower-*.f64`
4 488×	`lower-*.f32`
3 936×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	458	4000
1	1421	3369
2	4920	3299
0	8077	3108

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 236

Calls

Call 1

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

rewrite329.0ms (3.5%)

Memory

15.4MiB live, 517.2MiB allocated

Rules

4 754×	`lower-fma.f64`
4 754×	`lower-fma.f32`
4 464×	`lower-/.f32`
4 452×	`lower-/.f64`
4 092×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	234
0	61	221
1	272	200
2	1836	200
0	8416	180

Stop Event

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

Counts

20 → 588

Calls

Call 1

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

Outputs
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x))))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x)))))
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal -1/2 binary64) (neg.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) (neg.f64 (neg.f64 x)))
(pow.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x))) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1/2 binary64))
(.f64 (pow.f64 x #s(literal -3/4 binary64)) (.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))))
(.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/4 binary64))) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(exp.f64 (*.f64 #s(literal -3/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -3/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -3/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -3/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -3/4 binary64) (*.f64 (log.f64 x) #s(literal -3/4 binary64))))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 x)) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))))
(neg.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 (sqrt.f64 x)) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 x (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (neg.f64 (sqrt.f64 x)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 x (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (sqrt.f64 x)))
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (sqrt.f64 x))))
(pow.f64 x #s(literal -3/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -3 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -3/2 binary64)) (log.f64 x))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (sqrt.f64 x))))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 1/4 binary64))))
(exp.f64 (.f64 (log.f64 #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))))
(pow.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))
(.f64 (pow.f64 #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal -1/2 binary64)) (pow.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (.f64 (log.f64 #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))))
(/.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))))
(/.f64 (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))) #s(literal 1 binary64))
#s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))
(pow.f64 #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x)))) #s(literal -1 binary64))
(.f64 #s(approx ( (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))) #s(literal 1 binary64))
(+.f64 x (sqrt.f64 x))
(+.f64 (sqrt.f64 x) x)
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 x))) (/.f64 x (-.f64 x (sqrt.f64 x))))
(-.f64 (/.f64 x (-.f64 (sqrt.f64 x) x)) (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 x) x)))
(fma.f64 #s(literal 1 binary64) x (sqrt.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) x)
(fma.f64 x #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 x))
(fma.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) x)
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x) x)
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)) x)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x x x) (.f64 x (sqrt.f64 x))) (fma.f64 x (sqrt.f64 x) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (sqrt.f64 x)) (-.f64 (*.f64 x x) x)))
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(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) (fma.f64 x x (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))) (-.f64 #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))) x)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (.f64 (fma.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64)))) (*.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))
(.f64 (/.f64 (fma.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) x))))
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))

eval166.0ms (1.8%)

Memory: 27.1MiB live, 294.3MiB allocated
Compiler: Compiled 21 497 to 2 161 computations (89.9% saved)

prune187.0ms (2%)

Memory

-31.8MiB live, 356.3MiB allocated

Pruning

17 alts after pruning (11 fresh and 6 done)

	Pruned	Kept	Total
New	1 001	5	1 006
Fresh	2	6	8
Picked	3	2	5
Done	0	4	4
Total	1 006	17	1 023

Accuracy

100.0%

Counts

1 023 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64)))))
	42.1%	(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
	98.0%	(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	67.4%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x x)))))
✓	82.0%	(/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
✓	97.7%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
	81.3%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
	96.6%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
	7.8%	(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
	97.9%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
	96.6%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
✓	98.2%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))))
✓	65.7%	#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
	80.3%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
✓	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	97.9%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x)))
✓	5.4%	#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 707 to 234 computations (66.9% saved)

regimes40.0ms (0.4%)

Memory

-3.5MiB live, 35.2MiB allocated

Counts

38 → 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)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 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 #s(literal 1 binary64) (.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))) (sqrt.f64 (+.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)))))
(-.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) (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))
(/.f64 #s(approx (- (sqrt (+ 1 x)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) x (sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x x)))))
(/.f64 (/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x))))
(/.f64 #s(literal 1 binary64) (*.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (fma.f64 x x x))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (sqrt.f64 (fma.f64 x x x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (fma.f64 x x x)))
(*.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) x))
(/.f64 (*.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x x)))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 x (sqrt.f64 x))) (/.f64 (+.f64 x #s(literal -1 binary64)) (sqrt.f64 x))) x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1 binary64)) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))))

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

Calls

2 calls:

29.0ms	x
9.0ms	(-.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
98.9%	1	`x`
98.9%	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)

regimes11.0ms (0.1%)

Memory

-16.3MiB live, 24.1MiB allocated

Counts

15 → 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)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(approx (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (.f64 (/.f64 #s(approx (+ (/ (+ ( x 1/4) 1) (* x (sqrt x))) (/ (+ x -1) (sqrt x))) (sqrt.f64 x)) x) (/.f64 #s(literal 1/2 binary64) x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(approx (sqrt (+ (* x x) x)) (+.f64 x #s(literal 1/2 binary64))))

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

Calls

2 calls:

5.0ms	(-.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
98.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
98.0%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes7.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

9 → 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)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) (sqrt.f64 x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))

Outputs
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) 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
97.9%	1	`x`
97.9%	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

14.6MiB live, 14.6MiB 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)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))
#s(approx (/ (/ (- (+ 1 x) x) (+ x (sqrt (+ (* x x) x)))) (sqrt (+ 1 x))) (/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x))))
#s(approx (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (/.f64 (.f64 #s(literal 1/2 binary64) #s(approx (- (+ ( (sqrt (/ 1 (* x (* x x)))) (+ (* x 1/4) 1)) (sqrt x)) (sqrt (/ 1 x))) (sqrt.f64 x))) (*.f64 x x)))

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

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
96.6%	1	`x`
96.6%	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

-26.4MiB live, 12.6MiB 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)))
(/.f64 #s(literal 1 binary64) (.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) (+.f64 x #s(approx (sqrt (+ ( x x) x)) (+.f64 #s(literal 1/2 binary64) x)))))
(/.f64 #s(literal 1 binary64) #s(approx (* (+ (sqrt x) (sqrt (+ 1 x))) (sqrt (+ (* x x) x))) (+.f64 x (sqrt.f64 x))))

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

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
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)

regimes3.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 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)))

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

Calls

2 calls:

1.0ms	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
5.4%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
5.4%	1	`x`

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify6.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	131
1	53	131

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (13.6%)

Memory

6.2MiB live, 1 187.6MiB allocated

Rules

23 172×	`lower-fma.f64`
23 172×	`lower-fma.f32`
16 698×	`lower-fma.f64`
16 698×	`lower-fma.f32`
13 166×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	458	4000
1	1421	3369
2	4920	3299
0	8077	3108
0	562	4315
1	1784	3789
2	6200	3779
0	8123	3550
0	114	529
1	303	480
2	925	455
3	3326	445
0	8140	416
0	490	3730
1	1465	3220
2	4803	3185
0	8736	2997
0	8	23
0	14	23
1	66	19
2	565	19
3	6719	19
0	8113	19
0	49	259
0	76	249
1	322	214
2	2876	213
0	9344	205
0	40	234
0	61	221
1	272	200
2	1836	200
0	8416	180
0	37	245
0	63	233
1	302	188
2	2636	183
0	8750	180

Stop Event

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

Compiler

Compiled 250 to 130 computations (48% saved)

preprocess73.0ms (0.8%)

Memory: 9.0MiB live, 212.2MiB allocated
Compiler: Compiled 182 to 88 computations (51.6% 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%)

sample2.0s (21.2%)

explain166.0ms (1.8%)

preprocess26.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize50.0ms (0.5%)

series7.0ms (0.1%)

simplify288.0ms (3%)

rewrite239.0ms (2.5%)

eval37.0ms (0.4%)

prune59.0ms (0.6%)

simplify218.0ms (2.3%)

localize257.0ms (2.7%)

series23.0ms (0.2%)

simplify282.0ms (3%)

rewrite286.0ms (3%)

eval337.0ms (3.6%)

prune210.0ms (2.2%)

simplify203.0ms (2.1%)

localize269.0ms (2.8%)

series29.0ms (0.3%)

simplify306.0ms (3.2%)

rewrite336.0ms (3.5%)

eval310.0ms (3.3%)

prune593.0ms (6.3%)

simplify189.0ms (2%)

localize235.0ms (2.5%)

series13.0ms (0.1%)

simplify359.0ms (3.8%)

rewrite329.0ms (3.5%)

eval166.0ms (1.8%)

prune187.0ms (2%)

regimes40.0ms (0.4%)

regimes11.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

simplify6.0ms (0.1%)

soundness1.3s (13.6%)

preprocess73.0ms (0.8%)

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