Metrics for 2sqrt (example 3.1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.9s (28%)

Memory

21.2MiB live, 1 981.3MiB allocated

Samples

1.4s	7 990×	1	valid
18.0ms	266×	0	valid

Precisions

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

ival-add: 314.0ms (28.7% of total)

ival-sqrt: 246.0ms (22.5% of total)

adjust: 169.0ms (15.4% of total)

const: 157.0ms (14.3% of total)

ival-sub: 101.0ms (9.2% of total)

ival->: 59.0ms (5.4% of total)

ival-<: 26.0ms (2.4% of total)

ival-and: 12.0ms (1.1% of total)

exact: 8.0ms (0.7% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

explain334.0ms (4.9%)

Memory

15.0MiB live, 133.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
254	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	254	1

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	1	1

Precision?

0.996078431372549

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms	502×	1	valid
0.0ms	10×	0	valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-sqrt: 18.0ms (48.4% of total)

adjust: 8.0ms (21.5% of total)

ival-add: 6.0ms (16.1% of total)

ival-sub: 5.0ms (13.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess23.0ms (0.3%)

Memory

-5.4MiB live, 32.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated
Compiler: Compiled 7 to 6 computations (14.3% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize36.0ms (0.5%)

Memory

-4.1MiB live, 71.6MiB 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	(sqrt.f64 x)
accuracy	60.38998318043002	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

29.0ms	251×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sqrt: 10.0ms (48.4% of total)

adjust: 5.0ms (24.2% of total)

ival-add: 3.0ms (14.5% of total)

ival-sub: 2.0ms (9.7% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

4 → 48

Calls

Call 1

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

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (sqrt.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x))
1.0ms	x	@	inf	((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x))
1.0ms	x	@	0	((- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (sqrt x))

simplify175.0ms (2.6%)

Memory

14.3MiB live, 211.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	498
1	299	446
2	804	442
3	2258	434
4	4622	434
0	8210	398

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite148.0ms (2.2%)

Memory

-7.1MiB live, 226.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16

Stop Event

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

Counts

4 → 357

Calls

Call 1

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

Outputs
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eval53.0ms (0.8%)

Memory: -6.8MiB live, 112.1MiB allocated
Compiler: Compiled 7 775 to 1 415 computations (81.8% saved)

prune12.0ms (0.2%)

Memory

-1.2MiB live, 38.0MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	398	7	405
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	398	8	406

Accuracy

99.9%

Counts

406 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.5%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
	5.5%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	3.8%	(-.f64 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
▶	4.3%	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	98.7%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 183 to 142 computations (22.4% saved)

simplify69.0ms (1%)

Memory

14.4MiB live, 53.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 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 1/2 binary64))
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	#s(approx (+ x 1) x)
cost-diff	0	(sqrt.f64 #s(approx (+ x 1) x))
cost-diff	0	(-.f64 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
cost-diff	0	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
cost-diff	0	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
cost-diff	0	(/.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)
cost-diff	0	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	161
0	39	161
1	53	161
2	60	161
3	78	161
4	105	161
5	156	161
6	257	161
7	332	161
8	463	161
9	516	161
10	560	161
11	582	161
12	635	161
13	782	161
14	1066	161
15	1212	161
16	1772	161
17	2282	161
18	2365	161
19	2391	161
20	2406	161
21	2412	161
0	2412	161

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize93.0ms (1.4%)

Memory

-1.2MiB live, 156.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
accuracy	0.1484375	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.807436711509293	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
accuracy	0	(sqrt.f64 #s(approx (+ x 1) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.863325106466592	#s(approx (+ x 1) x)
accuracy	60.38998318043002	(-.f64 (sqrt.f64 #s(approx (+ x 1) x)) (sqrt.f64 x))
accuracy	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	59.6648625596574	#s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
accuracy	60.38998318043002	(-.f64 #s(approx (sqrt (+ x 1)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	59.68145524047697	#s(approx (sqrt (+ x 1)) #s(literal 1 binary64))
accuracy	60.38998318043002	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
accuracy	0.00390625	(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0.1484375	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.2421875	(/.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)
accuracy	0.5724270545718386	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))

Samples

74.0ms	251×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 287 to 45 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-add: 11.0ms (24.3% of total)

ival-sqrt: 11.0ms (24.3% of total)

adjust: 8.0ms (17.7% of total)

ival-mult: 8.0ms (17.7% of total)

ival-div: 5.0ms (11% of total)

ival-sub: 2.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.2%)

Memory

-21.8MiB live, 19.2MiB allocated

Counts

16 → 192

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (/ 1 x))
2.0ms	x	@	0	((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (/ 1 x))
1.0ms	x	@	inf	((- (sqrt (+ x 1)) (sqrt x)) (/ (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) x) (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (sqrt (/ 1 x)) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (sqrt x) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ (* 1/2 x) 1) (- (sqrt (+ x 1)) (sqrt x)) (sqrt (+ x 1)) (+ x 1) (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt (/ 1 x)) 1/2) (/ 1 x))

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

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

1.0ms

inf

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

simplify254.0ms (3.8%)

Memory

15.4MiB live, 217.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	2445
1	363	2160
2	1033	2142
3	2913	2114
4	5976	2114
0	8009	1943

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

rewrite151.0ms (2.2%)

Memory

-3.8MiB live, 151.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	131
0	39	131
1	149	123
2	1072	123
0	8364	120

Stop Event

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

Counts

16 → 435

Calls

Call 1

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

Outputs
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eval99.0ms (1.5%)

Memory: 30.0MiB live, 183.3MiB allocated
Compiler: Compiled 20 896 to 1 946 computations (90.7% saved)

prune46.0ms (0.7%)

Memory

-9.5MiB live, 116.6MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	784	3	787
Fresh	0	2	2
Picked	3	2	5
Done	0	1	1
Total	787	8	795

Accuracy

100.0%

Counts

795 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.5%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
▶	5.5%	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	4.3%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	98.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
▶	98.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 188 to 140 computations (25.5% saved)

simplify209.0ms (3.1%)

Memory

0.1MiB live, 203.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	201
0	47	197
1	69	193
2	89	193
3	112	193
4	151	193
5	227	193
6	351	193
7	529	193
8	777	193
9	1465	193
10	3116	193
11	6478	193
0	8106	187

Stop Event

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

Calls

Call 1

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

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

localize126.0ms (1.9%)

Memory

8.3MiB live, 165.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0.0078125	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.2578125	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	60.3033164726817	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.515625	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	60.38998318043002	(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.26171875	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
accuracy	0.807436711509293	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
accuracy	0	(sqrt.f64 x)
accuracy	0.889025730663778	#s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))
accuracy	59.6648625596574	#s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x)))
accuracy	60.38998318043002	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
accuracy	0	(sqrt.f64 x)
accuracy	0.2421875	(/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
accuracy	0.5724270545718386	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
accuracy	0.8136199988459661	#s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))

Samples

96.0ms	251×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 346 to 61 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-add: 21.0ms (28.9% of total)

ival-div: 14.0ms (19.2% of total)

adjust: 13.0ms (17.9% of total)

ival-sqrt: 12.0ms (16.5% of total)

ival-sub: 7.0ms (9.6% of total)

ival-mult: 6.0ms (8.2% of total)

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

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

exact: 0.0ms (0% of total)

series21.0ms (0.3%)

Memory

-16.8MiB live, 20.3MiB allocated

Counts

18 → 216

Calls

Call 1

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

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

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

3.0ms

inf

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

2.0ms

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

simplify176.0ms (2.6%)

Memory

8.5MiB live, 161.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	2789
1	665	2482
2	2067	2452
3	6478	2451
0	8024	2272

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

rewrite160.0ms (2.4%)

Memory

23.8MiB live, 180.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	176
0	47	170
1	207	160
2	1637	152
0	8769	146

Stop Event

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

Counts

18 → 793

Calls

Call 1

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

Outputs
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eval266.0ms (3.9%)

Memory: 13.2MiB live, 364.2MiB allocated
Compiler: Compiled 42 893 to 3 754 computations (91.2% saved)

prune44.0ms (0.6%)

Memory

-29.9MiB live, 92.9MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 721	2	1 723
Fresh	0	0	0
Picked	2	3	5
Done	0	3	3
Total	1 723	8	1 731

Accuracy

100.0%

Counts

1 731 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	4.3%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
▶	99.3%	(*.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)))
✓	98.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓	98.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 121 to 90 computations (25.6% saved)

simplify184.0ms (2.7%)

Memory

15.8MiB live, 162.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
cost-diff	0	#s(approx (- (+ 1 x) x) #s(literal 1 binary64))
cost-diff	0	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(+.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	0	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
cost-diff	7552	(*.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	105
0	26	105
1	42	85
2	67	85
3	79	85
4	154	85
5	384	85
6	1382	85
7	4010	85
8	5571	85
0	8113	82

Stop Event

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

Calls

Call 1

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

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

localize130.0ms (1.9%)

Memory

-14.1MiB live, 87.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0	#s(approx (- (+ 1 x) x) #s(literal 1 binary64))
accuracy	0.0078125	(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
accuracy	0.2578125	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
accuracy	0.0078125	(pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64))
accuracy	0.0078125	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
accuracy	0.3515625	(*.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)))
accuracy	0.515625	(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Samples

82.0ms	239×	1	valid
2.0ms	17×	0	valid

Compiler

Compiled 208 to 33 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-div: 34.0ms (50% of total)

ival-add: 9.0ms (13.2% of total)

adjust: 9.0ms (13.2% of total)

ival-sqrt: 5.0ms (7.4% of total)

ival-pow: 5.0ms (7.4% of total)

ival-mult: 3.0ms (4.4% of total)

ival-sub: 2.0ms (2.9% 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

10.3MiB live, 10.3MiB allocated

Counts

10 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

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

1.0ms

inf

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

simplify233.0ms (3.4%)

Memory

-3.9MiB live, 188.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	269	1732
1	792	1561
2	2315	1542
3	7937	1540
0	8785	1440

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite152.0ms (2.2%)

Memory

12.2MiB live, 167.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	87
0	26	77
1	117	69
2	908	49
0	9653	49

Stop Event

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

Counts

10 → 1 198

Calls

Call 1

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

Outputs
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eval454.0ms (6.7%)

Memory: -303.9MiB live, 421.3MiB allocated
Compiler: Compiled 73 648 to 5 515 computations (92.5% saved)

prune44.0ms (0.6%)

Memory

-14.5MiB live, 107.3MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	2 188	0	2 188
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	2 188	8	2 196

Accuracy

100.0%

Counts

2 196 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 #s(approx (- (+ 1 x) x) #s(literal 1 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	5.6%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	4.3%	(-.f64 #s(approx (sqrt (+ x 1)) #s(approx (+ (* 1/2 x) 1) (*.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 x))
✓	1.6%	(-.f64 #s(approx (sqrt (+ x 1)) #s(literal 1 binary64)) (sqrt.f64 x))
✓	99.3%	(*.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (pow.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) #s(literal -1 binary64)))
✓	98.4%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(approx (+ (* (sqrt (/ 1 x)) -1/8) (* 1/2 (sqrt x))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x))
✓	98.3%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
✓	98.5%	#s(approx (- (sqrt (+ x 1)) (sqrt x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))

Compiler

Compiled 307 to 154 computations (49.8% saved)

regimes9.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.1%)

Memory

-29.0MiB live, 9.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.3%	1	`x`
98.3%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

2 calls:

2.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
4.3%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
4.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify25.0ms (0.4%)

Memory

-2.4MiB live, 37.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	67
1	39	67
2	44	67
3	46	67
4	47	67

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.1s (15.5%)

Memory

-13.6MiB live, 538.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	228	2789
1	665	2482
2	2067	2452
3	6478	2451
0	8024	2272
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	135	2445
1	363	2160
2	1033	2142
3	2913	2114
4	5976	2114
0	8009	1943
0	113	498
1	299	446
2	804	442
3	2258	434
4	4622	434
0	8210	398
0	25	131
0	39	131
1	149	123
2	1072	123
0	8364	120

Stop Event

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

Compiler

Compiled 146 to 86 computations (41.1% saved)

preprocess41.0ms (0.6%)

Memory: 40.9MiB live, 79.1MiB allocated
Compiler: Compiled 158 to 84 computations (46.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

start0.0ms (0%)

analyze2.0ms (0%)

sample1.9s (28%)

explain334.0ms (4.9%)

preprocess23.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize36.0ms (0.5%)

series5.0ms (0.1%)

simplify175.0ms (2.6%)

rewrite148.0ms (2.2%)

eval53.0ms (0.8%)

prune12.0ms (0.2%)

simplify69.0ms (1%)

localize93.0ms (1.4%)

series14.0ms (0.2%)

simplify254.0ms (3.8%)

rewrite151.0ms (2.2%)

eval99.0ms (1.5%)

prune46.0ms (0.7%)

simplify209.0ms (3.1%)

localize126.0ms (1.9%)

series21.0ms (0.3%)

simplify176.0ms (2.6%)

rewrite160.0ms (2.4%)

eval266.0ms (3.9%)

prune44.0ms (0.6%)

simplify184.0ms (2.7%)

localize130.0ms (1.9%)

series7.0ms (0.1%)

simplify233.0ms (3.4%)

rewrite152.0ms (2.2%)

eval454.0ms (6.7%)

prune44.0ms (0.6%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

simplify25.0ms (0.4%)

soundness1.1s (15.5%)

preprocess41.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18