Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, B

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample584.0ms (9.6%)

Memory

31.3MiB live, 1 258.2MiB allocated

Samples

366.0ms	8 251×	0	valid
1.0ms	5×	2	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 218.0ms

ival-add: 87.0ms (39.8% of total)

ival-sqrt: 62.0ms (28.4% of total)

ival-div: 56.0ms (25.6% of total)

ival-true: 6.0ms (2.7% of total)

exact: 5.0ms (2.3% of total)

ival-assert: 3.0ms (1.4% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain82.0ms (1.4%)

Memory

-9.1MiB live, 147.3MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

27.0ms	510×	0	valid
0.0ms	2×	2	valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-add: 5.0ms (36.7% of total)

ival-sqrt: 4.0ms (29.3% of total)

ival-div: 3.0ms (22% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess24.0ms (0.4%)

Memory

-14.8MiB live, 27.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	14	23
0	14	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize23.0ms (0.4%)

Memory

1.2MiB live, 38.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.1796875	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

17.0ms	255×	0	valid
0.0ms	1×	2	valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 7.0ms (58.5% of total)

ival-add: 3.0ms (25.1% of total)

ival-sqrt: 2.0ms (16.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))
2.0ms	x	@	inf	((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))
0.0ms	x	@	0	((/ x (+ 1 (sqrt (+ x 1)))) (+ 1 (sqrt (+ x 1))) (sqrt (+ x 1)) (+ x 1))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

0.0ms

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

simplify207.0ms (3.4%)

Memory

1.1MiB live, 202.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	600
1	485	505
2	1630	483
3	5408	474
0	8354	430

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

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

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

rewrite272.0ms (4.5%)

Memory

-12.2MiB live, 233.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20

Stop Event

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

Counts

4 → 474

Calls

Call 1

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

Outputs
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eval87.0ms (1.4%)

Memory: -2.0MiB live, 154.1MiB allocated
Compiler: Compiled 9 770 to 2 141 computations (78.1% saved)

prune35.0ms (0.6%)

Memory

14.9MiB live, 54.0MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	510	10	520
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	510	11	521

Accuracy

100.0%

Counts

521 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	67.8%	(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
▶	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))
	89.1%	(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	40.3%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	33.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
▶	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
▶	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
▶	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
	34.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 176 to 140 computations (20.5% saved)

simplify126.0ms (2.1%)

Memory

-23.9MiB live, 138.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	128	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	0	(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff	0	(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	142
0	41	142
1	62	141
2	100	139
3	157	139
4	277	139
5	338	139
6	420	139
7	567	139
8	823	139
9	998	139
10	1248	139
11	2354	139
12	2942	139
13	3289	139
14	3325	139
15	3325	139
0	3325	139

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))
#s(literal 1 binary64)
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
x
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
x
#s(literal 1/2 binary64)
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(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)))
#s(literal 1 binary64)
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
x

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

localize141.0ms (2.3%)

Memory

9.2MiB live, 244.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	37.98336434559666	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0	(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
accuracy	0	(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
accuracy	0.05078125	(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
accuracy	20.934988222181097	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
accuracy	0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
accuracy	0.01171875	(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
accuracy	21.961888165757486	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	21.34919853464936	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0.109375	(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)
accuracy	0.1796875	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))

Samples

34.0ms	97×	1	valid
29.0ms	60×	2	valid
19.0ms	98×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 130 to 27 computations (79.2% saved)

Precisions

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

adjust: 11.0ms (19.9% of total)

ival-add: 11.0ms (19.9% of total)

ival-div: 10.0ms (18.1% of total)

ival-mult: 8.0ms (14.5% of total)

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

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

ival-sub: 2.0ms (3.6% of total)

exact: 1.0ms (1.8% of total)

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

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

series17.0ms (0.3%)

Memory

-10.9MiB live, 32.7MiB allocated

Counts

16 → 192

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) (patch (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (patch (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation binary64>) () ())
#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 #s(literal 1 binary64) (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>) () ())

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))
2.0ms	x	@	inf	((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))
2.0ms	x	@	0	((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))

Time

Variable

Point

Expression

4.0ms

-inf

((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))

2.0ms

inf

((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))

2.0ms

((/ 1 (/ (+ (sqrt (+ 1 x)) 1) x)) (/ (+ (sqrt (+ 1 x)) 1) x) (+ (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (/ x (+ 1 (sqrt (+ x 1)))) (* x 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* -1/8 x) 1/2) x) (+ (* -1/8 x) 1/2) (/ x (+ 1 (sqrt (+ x 1)))) (* (+ (* (+ (* 1/16 x) -1/8) x) 1/2) x) (+ (* (+ (* 1/16 x) -1/8) x) 1/2) (+ (* 1/16 x) -1/8) (neg (- 1 (sqrt (+ 1 x)))) (- 1 (sqrt (+ 1 x))) (+ 1 x))

simplify178.0ms (2.9%)

Memory

12.3MiB live, 204.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	277	2167
1	829	1862
2	2764	1777
3	7520	1777
0	8422	1647

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 190

Calls

Call 1

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

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

rewrite195.0ms (3.2%)

Memory

18.7MiB live, 253.1MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	122
0	41	120
1	179	119
2	1155	119
0	8386	119

Stop Event

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

Counts

16 → 701

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x))
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x)
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(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 #s(literal 1 binary64) x)

Outputs
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eval136.0ms (2.2%)

Memory: -0.1MiB live, 308.3MiB allocated
Compiler: Compiled 19 630 to 3 355 computations (82.9% saved)

prune36.0ms (0.6%)

Memory

19.4MiB live, 101.1MiB allocated

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	1 026	4	1 030
Fresh	1	4	5
Picked	2	3	5
Done	0	1	1
Total	1 029	12	1 041

Accuracy

100.0%

Counts

1 041 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	66.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
	40.3%	(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	89.1%	(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
▶	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
	33.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
▶	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
▶	34.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 173 to 140 computations (19.1% saved)

simplify155.0ms (2.6%)

Memory

-11.9MiB live, 160.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 #s(literal -1/8 binary64) x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
cost-diff	0	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
cost-diff	0	(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))
cost-diff	0	(/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	216
0	60	212
1	97	212
2	167	212
3	335	212
4	600	212
5	1098	212
6	1672	212
7	2388	212
8	3945	212
9	6140	212
10	7674	212
0	8003	208

Stop Event

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

Calls

Call 1

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

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

localize132.0ms (2.2%)

Memory

4.4MiB live, 224.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64))
accuracy	0.03125	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
accuracy	0.0703125	(fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64))
accuracy	21.608993743382083	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x)
accuracy	0.03515625	(fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))
accuracy	20.781235191229833	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0	(*.f64 #s(literal -1/8 binary64) x)
accuracy	0.00390625	(fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))
accuracy	21.665077371986023	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(sqrt.f64 x)
accuracy	17.942968362166226	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
accuracy	0.0078125	(-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.0078125	(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))
accuracy	0.109375	(*.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	6.758034600745224	(/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)))

Samples

57.0ms	147×	0	valid
37.0ms	96×	0	invalid
5.0ms	4×	2	valid
4.0ms	9×	1	valid

Compiler

Compiled 195 to 39 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-mult: 37.0ms (47.3% of total)

ival-add: 19.0ms (24.3% of total)

ival-pow: 11.0ms (14.1% of total)

ival-sqrt: 5.0ms (6.4% of total)

ival-div: 4.0ms (5.1% of total)

adjust: 1.0ms (1.3% of total)

ival-sub: 1.0ms (1.3% of total)

exact: 1.0ms (1.3% of total)

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

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

series36.0ms (0.6%)

Memory

10.6MiB live, 55.3MiB allocated

Counts

19 → 228

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())
#s(alt (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) (patch (/.f64 x (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (patch (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (patch (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/8 binary64) x) (patch (.f64 #s(literal -1/8 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) x) (patch (.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)) (patch (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) (patch (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (patch (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) (patch (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())

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

3 calls:

Time

Variable

Point

Expression

21.0ms

-inf

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

5.0ms

inf

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

2.0ms

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

simplify419.0ms (6.9%)

Memory

-158.2MiB live, 301.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	409	2902
1	1258	2547
2	4303	2422
0	8426	2264

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

rewrite201.0ms (3.3%)

Memory

15.8MiB live, 203.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	182
0	60	178
1	263	178
2	1927	178
0	8769	174

Stop Event

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

Counts

19 → 452

Calls

Call 1

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

Outputs
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eval124.0ms (2%)

Memory: -4.1MiB live, 191.6MiB allocated
Compiler: Compiled 16 978 to 2 309 computations (86.4% saved)

prune19.0ms (0.3%)

Memory

18.2MiB live, 56.2MiB allocated

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	693	1	694
Fresh	0	3	3
Picked	1	4	5
Done	0	4	4
Total	694	12	706

Accuracy

100.0%

Counts

706 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	66.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
▶	40.3%	(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
▶	89.1%	(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
✓	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
▶	33.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
✓	34.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 103 to 80 computations (22.3% saved)

simplify314.0ms (5.2%)

Memory

-18.7MiB live, 103.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64))
cost-diff	0	(/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
cost-diff	0	(+.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
cost-diff	0	(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff	0	(/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	131
0	42	131
1	65	131
2	114	129
3	213	129
4	399	129
5	711	129
6	1580	129
7	2706	129
8	3377	129
9	3817	129
10	4012	129
11	4102	129
12	4160	129
13	4439	129
14	4706	129
15	5146	129
16	5493	129
17	5675	129
18	5751	129
19	5751	129
20	5889	129
21	6482	129
22	6790	129
23	7238	129
0	8022	129

Stop Event

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

Calls

Call 1

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

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

localize159.0ms (2.6%)

Memory

26.0MiB live, 186.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)
accuracy	0.1171875	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
accuracy	20.600795801254243	#s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.00390625	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	16.380950392556315	(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.0078125	(-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.06640625	(fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy	0.109375	(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	6.754128350745224	(/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy	0	(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	18.243029700705332	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))

Samples

78.0ms	96×	0	invalid
31.0ms	26×	2	valid
15.0ms	43×	1	valid
13.0ms	90×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 125 to 24 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 121.0ms

ival-add: 95.0ms (78.5% of total)

ival-div: 8.0ms (6.6% of total)

ival-sqrt: 6.0ms (5% of total)

adjust: 5.0ms (4.1% of total)

ival-mult: 4.0ms (3.3% of total)

ival-sub: 2.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory

-15.4MiB live, 22.2MiB allocated

Counts

14 → 168

Calls

Call 1

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

Outputs
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) (patch #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (sqrt x) 1) (taylor 0 x) (#s(alt (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) (patch (-.f64 (sqrt.f64 x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -3/8 x))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 3/16 x) 3/8)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 3/16 (* -7/128 x))) 3/8)))) (taylor 0 x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* 3/2 x)) (taylor 0 x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 3/2 (* 3/8 x)))) (taylor 0 x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x)))))) (taylor 0 x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 1/2 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 (* x (+ 1/2 (* -1/8 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 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (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 (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (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 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 x) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* -1/8 x))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8)))) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 2 x) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* 1/2 x)) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x) (taylor 0 x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* 1/2 x)) (taylor 0 x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (sqrt (/ 1 x))) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (sqrt x)) (* -1 (/ (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2))) x))) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (+ (* -2 (sqrt x)) (* -1 (/ (+ (* -1 (/ (+ (* -2 (/ (* x (+ 1 (* 3/2 (sqrt x)))) (pow (sqrt -1) 2))) (* 3/2 (* (sqrt (pow x 3)) (/ (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (pow (sqrt -1) 2))))) x)) (+ (* -1/2 (/ x (pow (sqrt -1) 2))) (/ (* x (* (+ 1 (* 3/2 (sqrt x))) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (pow (sqrt -1) 2)))) x))) x)) (* (sqrt x) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (patch (.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (sqrt x)) (* -1 (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2))))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (/ (- (+ (* -1 (sqrt x)) (* -1 (/ (- (+ (* -1/2 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* (sqrt x) (/ (pow (+ 1 (* 3/2 (sqrt x))) 2) (pow (sqrt -1) 2)))) (* 3/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3)))) (/ (+ 1 (* 3/2 (sqrt x))) (* x (pow (sqrt -1) 2)))) x)) (taylor -inf x) (#s(alt (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (patch (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt 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>) () ())) ())
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#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (patch (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (- (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) 1) x)) (* (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 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1 (sqrt x)) (/ 1 (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) (patch (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) (patch #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (taylor -inf x) (#s(alt (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* 2 (/ 1 x))))) (taylor -inf x) (#s(alt (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ 2 (* 1/2 (sqrt (/ 1 x)))) x)) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ 2 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (patch (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

simplify255.0ms (4.2%)

Memory

13.8MiB live, 247.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	421	2345
1	1313	2025
2	4512	1920
0	8200	1767

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 164

Calls

Call 1

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

Outputs
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -3/8 x)))
(*.f64 (fma.f64 #s(literal -3/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 3/16 x) 3/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal -3/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 3/16 (* -7/128 x))) 3/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -7/128 binary64) x #s(literal 3/16 binary64)) x #s(literal -3/8 binary64)) x #s(literal 1/2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* 3/2 x))
(fma.f64 #s(literal 3/2 binary64) x #s(literal 2 binary64))
(+ 2 (* x (+ 3/2 (* 3/8 x))))
(fma.f64 (fma.f64 #s(literal 3/8 binary64) x #s(literal 3/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 3/2 (* x (+ 3/8 (* -1/16 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 3/8 binary64)) x #s(literal 3/2 binary64)) x #s(literal 2 binary64))
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)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* -1/8 x)))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 x))) 1/8))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (+ 2 (* 1/2 x)) x)
(/.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* -1/8 x)))) x)
(/.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)) x)
(/ (+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) x)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
(+ 2 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/8 x))))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (+ 1/8 (* -1/16 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/16 binary64) x #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(- (sqrt x) 1)
(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
(- (+ (sqrt x) (* -1 (/ (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))) (pow x 2)))) 1)
(fma.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(- (+ (sqrt x) (* 1/2 (/ 1 x))) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (+ (* -1 (* (sqrt (/ 1 (pow x 5))) (+ (* -1 (sqrt (pow x 3))) (* 1/2 (sqrt (pow x 3)))))) (* 1/2 (sqrt (/ 1 x)))))))
(-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(sqrt x)
(sqrt.f64 x)
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(* x (- (sqrt (/ 1 x)) (/ 1 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal -1 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) (- 1 (sqrt (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(+ (* 2 (sqrt (/ 1 x))) (* (sqrt x) (- 1 (sqrt (/ 1 x)))))
(+.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) #s(literal 2 binary64))))
(+ (* -1 (/ (+ (* 1/2 x) (* x (* (+ 1 (* 3/2 (sqrt x))) (- 1 (sqrt (/ 1 x)))))) (pow x 2))) (+ (* 2 (sqrt (/ 1 x))) (* (sqrt x) (- 1 (sqrt (/ 1 x))))))
(-.f64 (+.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 #s(literal 3/2 binary64) (sqrt.f64 x) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) x)))
(- (+ (* -1 (/ (+ (* 3/2 (* (sqrt (pow x 3)) (- 1 (sqrt (/ 1 x))))) (* 2 (* x (+ 1 (* 3/2 (sqrt x)))))) (pow x 3))) (+ (* 2 (sqrt (/ 1 x))) (* (sqrt x) (- 1 (sqrt (/ 1 x)))))) (+ (* 1/2 (/ 1 x)) (/ (* (+ 1 (* 3/2 (sqrt x))) (- 1 (sqrt (/ 1 x)))) x)))
(-.f64 (-.f64 (+.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1 binary64) (sqrt.f64 x) #s(literal 2 binary64)))) (fma.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (fma.f64 #s(literal 3/2 binary64) (sqrt.f64 x) #s(literal 1 binary64)) x) (/.f64 #s(literal 1/2 binary64) x))) (/.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) #s(literal 3/2 binary64) (.f64 (.f64 (fma.f64 #s(literal 3/2 binary64) (sqrt.f64 x) #s(literal 1 binary64)) x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ (+ (sqrt x) (* -1 (/ (+ x (* 3/2 (sqrt (pow x 3)))) (pow x 2)))) x)
(/.f64 (-.f64 (sqrt.f64 x) (/.f64 (fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 3/2 binary64) x) (*.f64 x x))) x)
(/ (- (+ (sqrt x) (* -3/2 (sqrt (/ 1 (pow x 3))))) (+ (* 3/2 (sqrt (/ 1 x))) (/ 1 x))) x)
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(/ (- (+ (sqrt x) (* -1 (/ (+ (* -1 (* (sqrt x) (* (+ 1 (* 3/2 (sqrt x))) (+ x (* 3/2 (sqrt (pow x 3))))))) (* 1/2 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4)))) (+ (* 3/2 (sqrt (/ 1 x))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (/ 1 x)))) x)
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(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)))
(-.f64 (/.f64 (fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (neg.f64 x)) x) (sqrt.f64 x))
(+ (* -1 (sqrt x)) (* -1 (/ (+ (* -1 (/ x (pow (sqrt -1) 2))) (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) (* 1/2 (/ x (pow (sqrt -1) 4)))) (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x))) x)))
(-.f64 (/.f64 (neg.f64 (-.f64 x (/.f64 (fma.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/2 binary64) (.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)))) x))) x) (sqrt.f64 x))
(* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (/ 1 x))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* 1/2 (sqrt (/ 1 x))) 1) x)))
(neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) x)))
(+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x)) 1) x)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)) x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x #s(literal 1 binary64))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1/2 (sqrt (/ 1 x)))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) x) x (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x))
(* -1 (* x (+ (* -1 (/ (+ 1 (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)) x)) x)
(* x (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(fma.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) x)
(* x (+ 1 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* 2 (/ 1 x)))))
(fma.f64 (-.f64 (/.f64 #s(literal 2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x x)
(* -1 (* x (- (* -1 (/ (+ 2 (* 1/2 (sqrt (/ 1 x)))) x)) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(*.f64 (+.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) #s(literal 2 binary64)) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (* x (- (* -1 (/ (+ 2 (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))) x)) (+ 1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)

rewrite165.0ms (2.7%)

Memory

7.9MiB live, 167.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	113
0	42	113
1	195	105
2	1393	105
0	8323	104

Stop Event

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

Counts

14 → 543

Calls

Call 1

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

Outputs
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eval278.0ms (4.6%)

Memory: -29.9MiB live, 211.1MiB allocated
Compiler: Compiled 19 872 to 2 563 computations (87.1% saved)

prune28.0ms (0.5%)

Memory

-8.6MiB live, 76.5MiB allocated

Pruning

15 alts after pruning (3 fresh and 12 done)

	Pruned	Kept	Total
New	840	3	843
Fresh	0	0	0
Picked	0	4	4
Done	0	8	8
Total	840	15	855

Accuracy

100.0%

Counts

855 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	66.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
✓	40.3%	(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
	6.3%	(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
	8.1%	(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
	4.6%	(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
✓	89.1%	(*.f64 (/.f64 x (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (-.f64 (+.f64 #s(literal 2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
✓	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
✓	33.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	66.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	67.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
✓	65.7%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	66.6%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
✓	34.5%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 290 to 170 computations (41.4% saved)

regimes15.0ms (0.3%)

Memory

8.3MiB live, 44.0MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	x
6.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes14.0ms (0.2%)

Memory

2.3MiB live, 38.8MiB allocated

Counts

15 → 2

Calls

Call 1

Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))

Outputs

#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))

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

Calls

2 calls:

8.0ms	x
5.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes10.0ms (0.2%)

Memory

27.6MiB live, 27.6MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ (sqrt (+ 1 x)) 1) #s(literal 2 binary64)) x))

Outputs

#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (*.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (*.f64 #s(literal 1/2 binary64) x)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes13.0ms (0.2%)

Memory

-24.1MiB live, 24.8MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x)))
(+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))
(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 x #s(literal 1/2 binary64) #s(literal 2 binary64))))
(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Outputs

#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x))

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

Calls

2 calls:

8.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
4.0ms	x

Results

Accuracy	Segments	Branch
99.7%	2	`x`
99.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes8.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

9 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.5%	2	`x`
99.5%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes8.0ms (0.1%)

Memory

-19.4MiB live, 19.0MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

5.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
3.0ms	x

Results

Accuracy	Segments	Branch
98.4%	2	`x`
98.4%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory

19.7MiB live, 19.7MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.4%	2	`x`
98.4%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes7.0ms (0.1%)

Memory

-16.6MiB live, 20.9MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
2.0ms	x

Results

Accuracy	Segments	Branch
97.9%	2	`x`
97.9%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
96.8%	2	`x`
96.8%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.1%)

Memory

-27.9MiB live, 10.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
66.6%	1	`x`
66.6%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.4754304874260255e-9	0.016407898855738474

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.4754304874260255e-9	0.016407898855738474

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.4754304874260255e-9	0.016407898855738474

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.4754304874260255e-9	0.016407898855738474

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02564718388093065	258.3458959985272

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02564718388093065	258.3458959985272

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02564718388093065	258.3458959985272

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02564718388093065	258.3458959985272

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify29.0ms (0.5%)

Memory

-8.5MiB live, 75.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	323
1	70	323
2	73	323
3	78	323

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))

Outputs
(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) x #s(literal 1/16 binary64)) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) x #s(literal 1/2 binary64)) x)) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3022314549036573/604462909807314587353088 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (.f64 #s(literal -1/8 binary64) x) x (.f64 #s(literal 1/2 binary64) x))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64))) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 3602879701896397/72057594037927936 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 #s(literal -1 binary64) #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)))
(+.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) #s(literal -1 binary64))

soundness1.3s (21.9%)

Memory

-2.7MiB live, 405.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	122
0	41	120
1	179	119
2	1155	119
0	8386	119
0	161	600
1	485	505
2	1630	483
3	5408	474
0	8354	430
0	421	2345
1	1313	2025
2	4512	1920
0	8200	1767
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20

Stop Event

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

Compiler

Compiled 519 to 250 computations (51.8% saved)

preprocess156.0ms (2.6%)

Memory: 19.6MiB live, 104.3MiB allocated
Compiler: Compiled 446 to 112 computations (74.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8

start0.0ms (0%)

analyze1.0ms (0%)

sample584.0ms (9.6%)

explain82.0ms (1.4%)

preprocess24.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize23.0ms (0.4%)

series6.0ms (0.1%)

simplify207.0ms (3.4%)

rewrite272.0ms (4.5%)

eval87.0ms (1.4%)

prune35.0ms (0.6%)

simplify126.0ms (2.1%)

localize141.0ms (2.3%)

series17.0ms (0.3%)

simplify178.0ms (2.9%)

rewrite195.0ms (3.2%)

eval136.0ms (2.2%)

prune36.0ms (0.6%)

simplify155.0ms (2.6%)

localize132.0ms (2.2%)

series36.0ms (0.6%)

simplify419.0ms (6.9%)

rewrite201.0ms (3.3%)

eval124.0ms (2%)

prune19.0ms (0.3%)

simplify314.0ms (5.2%)

localize159.0ms (2.6%)

series11.0ms (0.2%)

simplify255.0ms (4.2%)

rewrite165.0ms (2.7%)

eval278.0ms (4.6%)

prune28.0ms (0.5%)

regimes15.0ms (0.3%)

regimes14.0ms (0.2%)

regimes10.0ms (0.2%)

regimes13.0ms (0.2%)

regimes8.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify29.0ms (0.5%)

soundness1.3s (21.9%)

preprocess156.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	21
1	23	17
2	51	16
3	110	16
4	221	16
5	333	16
6	361	16
7	377	16
8	390	16
0	6	8
0	10	8
1	14	8
0	14	8