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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

3.2MiB live, 3.2MiB 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)

sample639.0ms (10.7%)

Memory

32.1MiB live, 1 286.7MiB allocated

Samples

426.0ms	8 254×	0	valid
0.0ms	2×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 244.0ms

ival-add: 100.0ms (41.1% of total)

ival-div: 67.0ms (27.5% of total)

ival-sqrt: 62.0ms (25.5% of total)

ival-true: 6.0ms (2.5% of total)

exact: 4.0ms (1.6% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain67.0ms (1.1%)

Memory

-0.5MiB live, 160.8MiB 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

25.0ms

512×

valid

Compiler

Compiled 59 to 22 computations (62.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 5.0ms (38% of total)

ival-sqrt: 4.0ms (30.4% of total)

ival-div: 3.0ms (22.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess19.0ms (0.3%)

Memory

-12.6MiB live, 28.0MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`associate-l`
42×	`distribute-lft-neg-in`
42×	`times-frac`
38×	`unsub-neg`
36×	`sub-neg`

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 9 to 6 computations (33.3% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB 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 9 to 6 computations (33.3% saved)

simplify3.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB 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)))))

Rules

8×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-+.f64`
4×	`+-commutative`
2×	`lift-sqrt.f64`

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)

localize18.0ms (0.3%)

Memory

5.2MiB live, 44.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
accuracy	0.0078125	(+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
accuracy	0.17578125	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Samples

14.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 3.0ms (40.7% of total)

ival-add: 3.0ms (40.7% of total)

ival-sqrt: 2.0ms (27.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

-26.0MiB live, 13.3MiB 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
3.0ms	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

3.0ms

-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))

simplify195.0ms (3.3%)

Memory

22.0MiB live, 213.2MiB allocated

Algorithm

1×	egg-herbie

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
3 776×	`lower-*.f64`
3 776×	`lower-*.f32`
2 642×	`lower-+.f64`

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 (.f64 (.f64 x x) x)) (/.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 (.f64 (*.f64 x x) x)) (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) (.f64 (.f64 x x) x))) #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) (.f64 (.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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 (.f64 (.f64 x x) x)) (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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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)

rewrite185.0ms (3.1%)

Memory

14.9MiB live, 174.3MiB allocated

Rules

3 950×	`lower-fma.f64`
3 950×	`lower-fma.f32`
3 308×	`lower-/.f32`
3 306×	`lower-/.f64`
2 908×	`lower-*.f64`

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

eval101.0ms (1.7%)

Memory: -20.3MiB live, 129.2MiB allocated
Compiler: Compiled 11 091 to 2 091 computations (81.1% saved)

prune79.0ms (1.3%)

Memory

27.4MiB live, 113.9MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	513	7	520
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	513	8	521

Accuracy

100.0%

Counts

521 → 8

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)))))
	64.0%	(/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64))))
	41.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	36.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
▶	65.0%	#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))
▶	63.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
▶	65.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
▶	36.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 115 to 74 computations (35.7% saved)

simplify10.0ms (0.2%)

Memory

-28.6MiB live, 8.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

132×	`lower-fma.f32`
126×	`lower-fma.f64`
70×	`lower-*.f32`
64×	`lower-*.f64`
64×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	122
0	33	122
1	49	122
2	68	122
3	103	122
4	137	122
5	140	122
0	140	122

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize292.0ms (4.9%)

Memory

-128.6MiB live, 80.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
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	22.2552964629123	#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	(-.f64 (sqrt.f64 x) #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	19.442877400773835	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
accuracy	0	(fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))
accuracy	0	(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
accuracy	23.26619693003524	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
accuracy	0	(sqrt.f64 x)
accuracy	19.205898199030145	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	21.90091619543074	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))

Samples

25.0ms	171×	0	valid
11.0ms	85×	0	invalid

Compiler

Compiled 102 to 22 computations (78.4% saved)

Precisions

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

ival-mult: 12.0ms (48.5% of total)

ival-add: 6.0ms (24.2% of total)

ival-sqrt: 3.0ms (12.1% of total)

ival-div: 2.0ms (8.1% of total)

ival-sub: 1.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#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)))) (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 #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 (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 #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>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

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

2.0ms

inf

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

simplify196.0ms (3.3%)

Memory

-7.4MiB live, 307.8MiB allocated

Algorithm

1×	egg-herbie

Rules

22 598×	`lower-fma.f64`
22 598×	`lower-fma.f32`
3 778×	`lower-*.f64`
3 778×	`lower-*.f32`
3 642×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	1477
1	375	1262
2	1258	1181
3	4133	1171
0	8363	1053

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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

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

rewrite194.0ms (3.2%)

Memory

11.0MiB live, 207.4MiB allocated

Rules

8 160×	`lower-fma.f32`
8 154×	`lower-fma.f64`
5 282×	`lower-*.f32`
5 276×	`lower-*.f64`
4 152×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	108
0	33	108
1	129	108
2	867	103
0	8371	103

Stop Event

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

Counts

13 → 397

Calls

Call 1

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

Outputs
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 #s(literal 1/2 binary64) x))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1/2 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (*.f64 (log.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 (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64)) x) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) x)))))
(.f64 (.f64 x (fma.f64 #s(literal 1/64 binary64) (*.f64 x x) #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))))
(.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) x)))))
(.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))) x))
(.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) x)))) x))
(.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x) #s(literal 1 binary64))
(*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
(*.f64 x (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/64 binary64) (.f64 x x))) x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) x)))
(/.f64 (.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64))) x) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64))) x) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/64 binary64) (.f64 x x)))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/8 binary64) x)))
(/.f64 (.f64 x (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)))) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (.f64 x (neg.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal -1/8 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x))) (-.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal -1/8 binary64)))) (-.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal -1/8 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) x) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal -1/8 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (.f64 x x) #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)) x)) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)))) (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)) x) (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)) x) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 #s(literal 1/64 binary64) x) #s(literal -1/16 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x))))
(/.f64 (.f64 x (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64))) (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)))
(/.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 x (-.f64 (*.f64 #s(literal 1/64 binary64) x) #s(literal -1/16 binary64)))))
(/.f64 (.f64 x (fma.f64 (.f64 #s(literal -1/512 binary64) (.f64 x x)) x #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal -1/16 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) x))) (.f64 (fma.f64 (.f64 #s(literal -1/512 binary64) (*.f64 x x)) x #s(literal 1/8 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/64 binary64) (.f64 x x) #s(literal -1/4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/16 binary64) x))) (.f64 x (fma.f64 (.f64 #s(literal -1/512 binary64) (*.f64 x x)) x #s(literal 1/8 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) x))
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(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal -1/16 binary64) x) #s(literal -1/8 binary64))
(fma.f64 #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) x) #s(literal -1/8 binary64))
(fma.f64 (.f64 #s(literal 1/256 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64))) (neg.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)))))
(fma.f64 (neg.f64 x) #s(literal -1/16 binary64) #s(literal -1/8 binary64))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64) #s(literal -1/8 binary64))
(fma.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1 binary64) #s(literal -1/8 binary64))
(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
(fma.f64 #s(literal -1/8 binary64) (neg.f64 (*.f64 #s(literal 1/2 binary64) x)) #s(literal -1/8 binary64))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/8 binary64) x) #s(literal -1/8 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/16 binary64) x))) (/.f64 (.f64 #s(literal 1/256 binary64) (.f64 x x)) (-.f64 #s(literal -1/8 binary64) (.f64 #s(literal 1/16 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/256 binary64) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) x #s(literal 1/8 binary64))) (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/256 binary64) (.f64 x x)) (fma.f64 #s(literal 1/16 binary64) x #s(literal 1/8 binary64))) (neg.f64 (/.f64 #s(literal -1/64 binary64) (fma.f64 #s(literal -1/16 binary64) x #s(literal -1/8 binary64)))))
(+.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) x))

eval79.0ms (1.3%)

Memory: 10.7MiB live, 126.4MiB allocated
Compiler: Compiled 10 721 to 1 198 computations (88.8% saved)

prune86.0ms (1.4%)

Memory

-13.2MiB live, 102.4MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	579	1	580
Fresh	1	1	2
Picked	0	5	5
Done	0	1	1
Total	580	8	588

Accuracy

100.0%

Counts

588 → 8

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)))))
▶	41.4%	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	65.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
✓	36.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	65.0%	#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))
✓	63.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	65.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
✓	36.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 64 to 41 computations (35.9% saved)

simplify122.0ms (2%)

Memory

9.2MiB live, 101.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 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	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64))
cost-diff	0	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))

Rules

1 608×	`lower-fma.f32`
1 604×	`lower-fma.f64`
680×	`lower-*.f32`
676×	`lower-*.f64`
406×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	28	67
1	45	64
2	77	64
3	135	64
4	229	64
5	264	64
6	285	64
7	305	64
8	335	64
9	394	64
10	647	64
11	1598	64
12	2114	64
13	2822	64
14	2826	64
15	2826	64
16	2827	64
0	2827	62

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize89.0ms (1.5%)

Memory

-15.8MiB live, 141.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(neg.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	37.527541847159775	(-.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.046875	(fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))
accuracy	22.40155624034634	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))

Samples

39.0ms	96×	1	valid
21.0ms	63×	2	valid
15.0ms	97×	0	valid

Compiler

Compiled 60 to 21 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-add: 25.0ms (40.8% of total)

adjust: 14.0ms (22.8% of total)

ival-sqrt: 10.0ms (16.3% of total)

ival-mult: 6.0ms (9.8% of total)

ival-div: 2.0ms (3.3% of total)

ival-neg: 2.0ms (3.3% of total)

ival-sub: 2.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify197.0ms (3.3%)

Memory

-3.8MiB live, 183.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 500×	`lower-fma.f64`
11 500×	`lower-fma.f32`
3 482×	`lower-+.f64`
3 482×	`lower-+.f32`
3 016×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	220	1036
1	658	920
2	2236	881
3	6254	872
0	8068	813

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

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

rewrite253.0ms (4.2%)

Memory

-15.4MiB live, 233.7MiB allocated

Rules

4 488×	`lower-*.f32`
4 484×	`lower-*.f64`
4 440×	`lower-fma.f32`
4 436×	`lower-fma.f64`
4 078×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	61
0	28	61
1	127	58
2	868	58
0	8478	55

Stop Event

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

Counts

9 → 393

Calls

Call 1

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

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

eval119.0ms (2%)

Memory: 28.3MiB live, 177.4MiB allocated
Compiler: Compiled 11 701 to 1 606 computations (86.3% saved)

prune57.0ms (0.9%)

Memory

24.2MiB live, 181.4MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	498	1	499
Fresh	0	0	0
Picked	1	1	2
Done	0	6	6
Total	499	8	507

Accuracy

100.0%

Counts

507 → 8

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)))))
▶	41.4%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
✓	65.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
✓	36.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	65.0%	#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))
✓	63.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	65.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
✓	36.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 63 to 40 computations (36.5% saved)

simplify5.0ms (0.1%)

Memory

-26.3MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

8×	`lower-+.f32`
6×	`lower-+.f64`
4×	`+-commutative`
2×	`lift-sqrt.f64`
2×	`lift-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	14	15
2	15	15
0	15	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.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)
#s(literal 1 binary64)
x

Outputs
(-.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))
#s(literal 1 binary64)
x

localize26.0ms (0.4%)

Memory

-3.3MiB live, 75.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	37.527541847159775	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))

Samples

8.0ms	65×	2	valid
8.0ms	94×	1	valid
4.0ms	97×	0	valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-sqrt: 4.0ms (34.5% of total)

adjust: 3.0ms (25.9% of total)

ival-add: 3.0ms (25.9% of total)

ival-sub: 2.0ms (17.2% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#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 (+.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 (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 (* 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 (* 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>) () ())) ())
#s(alt (* x (+ 1/2 (* x (- (* x (+ 1/16 (* -5/128 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>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 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 (sqrt x) (taylor inf 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 (* x (- (sqrt (/ 1 x)) (/ 1 x))) (taylor inf 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 (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (/ 1 x))) (taylor inf 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 (* 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 (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 x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 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 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<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 #s(literal 1 binary64) x)) (patch (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>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf 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 (* -1 (* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))) (taylor -inf 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 (* -1 (* x (+ (* -1 (/ (- (* -1/2 (sqrt (/ 1 x))) 1) x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf 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 (* -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 (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 (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (patch (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#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 #s(literal 1 binary64) x)) (patch (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
0.0ms	x	@	-inf	((- (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (+ 1 x))
0.0ms	x	@	inf	((- (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (+ 1 x))
0.0ms	x	@	0	((- (sqrt (+ 1 x)) 1) (sqrt (+ 1 x)) (+ 1 x))

simplify229.0ms (3.8%)

Memory

12.1MiB live, 169.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
3 902×	`lower-*.f64`
3 902×	`lower-*.f32`
2 204×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	415
1	312	375
2	912	358
3	2749	347
4	6280	347
0	8165	312

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 34

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
(+ 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)
(* 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) (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)))

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
#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)
(* 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) (.f64 (.f64 x x) x))) #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) (.f64 (.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (.f64 (*.f64 x x) x))) #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) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))) (neg.f64 x) #s(literal -1 binary64))
(* -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 #s(literal -1/2 binary64) (sqrt.f64 x))) x) #s(literal 1 binary64)))
(* -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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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) (.f64 (*.f64 x x) x))) (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)

rewrite180.0ms (3%)

Memory

5.0MiB live, 176.6MiB allocated

Rules

5 796×	`lower-fma.f64`
5 796×	`lower-fma.f32`
3 390×	`lower-*.f64`
3 390×	`lower-*.f32`
2 998×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	39	13
2	265	13
3	3291	13
0	8344	12

Stop Event

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

Counts

3 → 428

Calls

Call 1

Inputs
(-.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)

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

eval133.0ms (2.2%)

Memory: -3.4MiB live, 116.7MiB allocated
Compiler: Compiled 10 146 to 1 611 computations (84.1% saved)

prune193.0ms (3.2%)

Memory

-24.8MiB live, 104.1MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	460	2	462
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	460	10	470

Accuracy

100.0%

Counts

470 → 10

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)))))
✓	41.4%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
	7.0%	(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 1 binary64))
	4.6%	(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
✓	65.0%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x)))
✓	36.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	65.0%	#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))
✓	63.4%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x))
✓	65.3%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
✓	36.8%	#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (sqrt.f64 x))

Compiler

Compiled 160 to 79 computations (50.6% saved)

regimes9.0ms (0.1%)

Memory

20.0MiB live, 20.0MiB allocated

Counts

12 → 1

Calls

Call 1

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes90.0ms (1.5%)

Memory

-15.0MiB live, 22.2MiB allocated

Counts

11 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

85.0ms	(/.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 11 to 7 computations (36.4% saved)

regimes31.0ms (0.5%)

Memory

-19.0MiB live, 19.4MiB allocated

Counts

10 → 2

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes7.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 (sqrt.f64 (+.f64 #s(literal 1 binary64) 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))
(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 (sqrt.f64 (+.f64 #s(literal 1 binary64) 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
99.7%	2	`x`
99.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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 (sqrt.f64 (+.f64 #s(literal 1 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))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) 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
99.6%	2	`x`
99.6%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes24.0ms (0.4%)

Memory

-24.7MiB live, 16.4MiB allocated

Counts

6 → 2

Calls

Call 1

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

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:

20.0ms	x
3.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
98.9%	2	`x`
98.9%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
97.7%	2	`x`
97.7%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(-.f64 #s(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))
#s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 #s(approx (sqrt (+ 1 x)) (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 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	x
2.0ms	(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
97.3%	2	`x`
97.3%	2	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

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
65.3%	1	`x`
65.3%	1	`(/.f64 x (+.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes108.0ms (1.8%)

Memory

-32.9MiB live, 6.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

106.0ms	(/.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 11 to 7 computations (36.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.275763520691658e-7	0.0044762791116618105

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.275763520691658e-7	0.0044762791116618105

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.275763520691658e-7	0.0044762791116618105

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.275763520691658e-7	0.0044762791116618105

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0044762791116618105	25.367763091382507

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0044762791116618105	25.367763091382507

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0044762791116618105	25.367763091382507

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify8.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
8×	`*-commutative_binary64`
8×	`unsub-neg_binary64`
8×	`sub-neg_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	275
1	65	275
2	71	275
3	74	275
4	77	275
5	82	275

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 4722366482869645/4722366482869645213696 binary64)) (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)))) (-.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 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) 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 4722366482869645/4722366482869645213696 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 (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 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #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 4722366482869645/4722366482869645213696 binary64)) (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 x #s(approx (+ 1 (sqrt (+ x 1))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 2 binary64)))) (-.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 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (fma.f64 (fma.f64 #s(literal 1/16 binary64) x #s(literal -1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/2 binary64) 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 4722366482869645/4722366482869645213696 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 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 4722366482869645/4722366482869645213696 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 (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 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(if (<=.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) #s(literal 4722366482869645/4722366482869645213696 binary64)) #s(approx (/ x (+ 1 (sqrt (+ x 1)))) (*.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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 5764607523034235/1152921504606846976 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(approx (sqrt (+ 1 x)) #s(literal 1 binary64)) #s(literal 1 binary64))

soundness1.5s (25.8%)

Memory

-22.8MiB live, 625.4MiB allocated

Rules

18 662×	`lower-fma.f64`
18 662×	`lower-fma.f32`
16 374×	`lower-fma.f64`
16 374×	`lower-fma.f32`
8 160×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	61
0	28	61
1	127	58
2	868	58
0	8478	55
0	161	600
1	485	505
2	1630	483
3	5408	474
0	8354	430
0	6	21
0	10	21
1	46	21
2	315	20
3	3400	20
0	8278	20
0	22	108
0	33	108
1	129	108
2	867	103
0	8371	103
0	110	415
1	312	375
2	912	358
3	2749	347
4	6280	347
0	8165	312

Stop Event

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

Compiler

Compiled 456 to 190 computations (58.3% saved)

preprocess361.0ms (6%)

Memory: 21.4MiB live, 99.4MiB allocated
Compiler: Compiled 390 to 82 computations (79% 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%)

sample639.0ms (10.7%)

explain67.0ms (1.1%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize18.0ms (0.3%)

series6.0ms (0.1%)

simplify195.0ms (3.3%)

rewrite185.0ms (3.1%)

eval101.0ms (1.7%)

prune79.0ms (1.3%)

simplify10.0ms (0.2%)

localize292.0ms (4.9%)

series11.0ms (0.2%)

simplify196.0ms (3.3%)

rewrite194.0ms (3.2%)

eval79.0ms (1.3%)

prune86.0ms (1.4%)

simplify122.0ms (2%)

localize89.0ms (1.5%)

series7.0ms (0.1%)

simplify197.0ms (3.3%)

rewrite253.0ms (4.2%)

eval119.0ms (2%)

prune57.0ms (0.9%)

simplify5.0ms (0.1%)

localize26.0ms (0.4%)

series1.0ms (0%)

simplify229.0ms (3.8%)

rewrite180.0ms (3%)

eval133.0ms (2.2%)

prune193.0ms (3.2%)

regimes9.0ms (0.1%)

regimes90.0ms (1.5%)

regimes31.0ms (0.5%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes24.0ms (0.4%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes108.0ms (1.8%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.5s (25.8%)

preprocess361.0ms (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