Metrics for sqrt D (should all be same)

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample700.0ms (5.9%)

Memory

6.7MiB live, 797.6MiB allocated

Samples

514.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 266.0ms

ival-pow2: 141.0ms (53.1% of total)

ival-sqrt: 57.0ms (21.5% of total)

ival-mult: 54.0ms (20.3% of total)

ival-true: 5.0ms (1.9% of total)

exact: 5.0ms (1.9% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

preprocess18.0ms (0.2%)

Memory

-11.0MiB live, 27.9MiB allocated

Algorithm

1×	egg-herbie

Rules

70×	`associate-r`
46×	`associate-l`
38×	`distribute-rgt-neg-out`
38×	`unsub-neg`
34×	`distribute-lft-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

explain63.0ms (0.5%)

Memory

27.4MiB live, 73.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	2	(1.4097574924722788e-158)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	65	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	65
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	65
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	55	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	55
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	55

Confusion

	Predicted +	Predicted -
+	120	2
-	0	134

Precision

1.0

Recall

0.9836065573770492

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	2
-	0	0	134

Precision?

1.0

Recall?

0.9836065573770492

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

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

ival-pow2: 6.0ms (46.4% of total)

ival-mult: 3.0ms (23.2% of total)

ival-sqrt: 3.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune32.0ms (0.3%)

Memory

-35.8MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
✓	cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Rules

14×	`lower-*.f32`
12×	`lower-*.f64`
8×	`*-commutative`
2×	`lift-sqrt.f64`
2×	`lift-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	10	16
2	14	16
3	16	16
0	16	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
x

Outputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
x

localize19.0ms (0.2%)

Memory

26.8MiB live, 26.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
✓	accuracy	56.1%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-pow2: 3.0ms (45.8% of total)

ival-mult: 2.0ms (30.6% of total)

ival-sqrt: 2.0ms (30.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())

Inputs

#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())

#s(alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())

#s(alt (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())

Calls

9 calls:

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

simplify36.0ms (0.3%)

Memory

-29.8MiB live, 7.9MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))

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

rewrite141.0ms (1.2%)

Memory

39.8MiB live, 231.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 310×	`lower-*.f64`
2 310×	`lower-*.f32`
2 014×	`lower-/.f64`
2 014×	`lower-/.f32`
1 182×	`frac-times`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4

Stop Event

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

Counts

3 → 46

Calls

Call 1

Inputs
(pow.f64 x #s(literal 2 binary64))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Outputs
#s(literal 1 binary64)
x
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))))
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 #s(literal 1/2 binary64)))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (E.f64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (log.f64 #s(literal 4 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal -2 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
#s(literal 2 binary64)

eval18.0ms (0.1%)

Memory: -36.4MiB live, 18.7MiB allocated
Compiler: Compiled 599 to 120 computations (80% saved)

prune9.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Accuracy

99.6%

Counts

83 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
▶	5.4%	(sqrt.f64 #s(literal 2 binary64))
▶	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 24 to 17 computations (29.2% saved)

simplify9.0ms (0.1%)

Memory

-25.5MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	#s(approx (pow x 2) (*.f64 x x))
✓	cost-diff	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
✓	cost-diff	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Rules

42×	`lower-*.f32`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
36×	`lower-*.f64`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	20	78
1	32	78
2	45	78
3	56	78
4	68	78
5	80	78
6	91	78
7	111	78
8	116	78
0	116	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(literal 2 binary64)
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(literal 2 binary64)
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)
x

localize40.0ms (0.3%)

Memory

9.3MiB live, 87.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	#s(approx (pow x 2) (*.f64 x x))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
✓	accuracy	56.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.6%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Samples

22.0ms

256×

valid

Compiler

Compiled 57 to 11 computations (80.7% saved)

Precisions

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

ival-mult: 5.0ms (37.6% of total)

ival-sqrt: 4.0ms (30.1% of total)

ival-pow2: 3.0ms (22.6% of total)

ival-neg: 1.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt ( 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) (patch (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (pow x 2) (.f64 x x)) (patch #s(approx (pow x 2) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(neg (* x (sqrt 2)))
0.0ms	x	@	0	(neg (* x (sqrt 2)))
0.0ms	x	@	inf	(neg (* x (sqrt 2)))
0.0ms	x	@	0	(sqrt (* 2 (pow x 2)))
0.0ms	x	@	0	(sqrt (* 2 (pow x 2)))

simplify8.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite313.0ms (2.6%)

Memory

-10.2MiB live, 345.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`
2 986×	`lower-*.f64`
1 314×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	63
0	20	67
1	47	59
2	115	59
3	502	59
4	4969	57
0	8327	57

Stop Event

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

Counts

9 → 1 159

Calls

Call 1

Inputs
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
#s(approx (pow x 2) (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x)))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x)))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(fabs.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 x x) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (/.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) x #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (neg.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 #s(literal 3/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) x) (/.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x x)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) x) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) x)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) x) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 x x)) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (sqrt.f64 x)) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) x)) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) (.f64 #s(literal 2 binary64) (*.f64 x (sqrt.f64 x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x)) (/.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 0 binary64))
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(+.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 0 binary64))
(/.f64 #s(literal -2 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal 0 binary64) (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))))))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))) #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x)))) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
(pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 #s(literal 4 binary64) (.f64 #s(approx (pow x 2) (.f64 x x)) #s(approx (pow x 2) (.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 #s(approx (pow x 2) (.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (pow x 2) (.f64 x x)))))
(.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(approx (pow x 2) (*.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (*.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(approx (pow x 2) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/8 binary64)))
(.f64 (.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (pow x 2) (.f64 x x)))) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
(.f64 #s(literal 2 binary64) (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 2 binary64))
(.f64 (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))) #s(literal 2 binary64))
#s(approx (pow x 2) (*.f64 x x))
(+.f64 (*.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(fabs.f64 (neg.f64 (*.f64 x x)))
(fabs.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 x (.f64 x (*.f64 x x))))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 0 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 0 binary64)) (-.f64 (.f64 x x) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 8 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))))

eval441.0ms (3.7%)

Memory: -5.5MiB live, 429.0MiB allocated
Compiler: Compiled 30 881 to 1 701 computations (94.5% saved)

prune236.0ms (2%)

Memory

-18.5MiB live, 355.6MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	1 833	5	1 838
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 833	9	1 842

Accuracy

100.0%

Counts

1 842 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
▶	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
▶	50.3%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
▶	49.4%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 112 to 81 computations (27.7% saved)

simplify46.0ms (0.4%)

Memory

29.8MiB live, 67.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
✓	cost-diff	1280	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	128	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Rules

316×	`lower-*.f32`
312×	`lower-fma.f64`
312×	`lower-fma.f32`
306×	`lower-*.f64`
246×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	160
0	39	154
1	61	152
2	95	152
3	153	152
4	216	152
5	336	152
6	481	152
7	678	152
8	859	152
9	936	152
10	955	152
11	973	152
12	991	152
13	1010	152
14	1015	152
15	1016	152
0	1016	152

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize84.0ms (0.7%)

Memory

9.7MiB live, 163.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.8%	(/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	accuracy	99.8%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.7%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	accuracy	99.2%	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Samples

25.0ms	127×	0	valid
23.0ms	129×	0	invalid

Compiler

Compiled 123 to 23 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 12.0ms (40.5% of total)

ival-div: 6.0ms (20.3% of total)

ival-sqrt: 6.0ms (20.3% of total)

ival-pow2: 3.0ms (10.1% of total)

ival-neg: 1.0ms (3.4% of total)

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

exact: 0.0ms (0% of total)

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

series17.0ms (0.1%)

Memory

-4.8MiB live, 29.0MiB allocated

Counts

18 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

simplify273.0ms (2.3%)

Memory

-8.5MiB live, 234.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2 428×	`lower-*.f64`
2 428×	`lower-fma.f64`
2 428×	`lower-fma.f32`
2 428×	`lower-*.f32`
1 552×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	892
1	58	892
2	148	892
3	278	892
4	511	892
5	826	892
6	1371	892
7	1502	892
8	1626	892
9	1848	892
10	2084	892
11	2536	892
12	2612	892
13	2638	892
14	2642	892
15	2642	892
16	2642	892
17	2648	892
18	3452	892
19	4383	892
20	5272	892
21	5640	892
22	5842	892
23	5886	892
24	7017	892
25	7541	892
26	7696	892
0	8008	892

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

rewrite273.0ms (2.3%)

Memory

-10.2MiB live, 472.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 908×	`lower-*.f32`
2 898×	`lower-*.f64`
2 158×	`lower-fma.f64`
2 158×	`lower-fma.f32`
1 864×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	131
0	39	123
1	101	101
2	354	96
3	1825	90
0	8611	90

Stop Event

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

Counts

18 → 2 627

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
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(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
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(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
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(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (neg.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))))
(.f64 (.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (neg.f64 (neg.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))))
(.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (*.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (*.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (neg.f64 (*.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (.f64 (.f64 x #s(literal -2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (.f64 (.f64 #s(literal 2 binary64) x) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (.f64 (*.f64 x #s(literal -2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))
(.f64 (.f64 (*.f64 x #s(literal -2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (sqrt.f64 x))
(.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (*.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x))) (neg.f64 (sqrt.f64 x)))
(.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 (neg.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 (sqrt.f64 x))) (neg.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (pow.f64 (.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))))
(.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (sqrt.f64 (.f64 x (neg.f64 x))) (sqrt.f64 #s(literal -2 binary64)))
(.f64 (sqrt.f64 (.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (neg.f64 (.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (.f64 (.f64 x #s(literal -2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 #s(literal 2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))) (neg.f64 (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64)))))
(.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(.f64 (neg.f64 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (neg.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
(.f64 (neg.f64 (neg.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))) (*.f64 #s(literal -2 binary64) (pow.f64 #s(literal 2 binary64) #s(literal -1/4 binary64))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (neg.f64 (.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (neg.f64 (pow.f64 (.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(fabs.f64 (sqrt.f64 x))
(fabs.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(/.f64 (sqrt.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

eval470.0ms (4%)

Memory: 43.2MiB live, 638.5MiB allocated
Compiler: Compiled 43 310 to 3 139 computations (92.8% saved)

prune234.0ms (2%)

Memory

-6.0MiB live, 488.8MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	3 387	2	3 389
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	3 390	8	3 398

Accuracy

100.0%

Counts

3 398 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
✓	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
▶	50.1%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x))))
✓	49.4%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify7.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	(/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	(sqrt.f64 (*.f64 x #s(literal -2 binary64)))
✓	cost-diff	(.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))
✓	cost-diff	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x))))

Rules

34×	`lower-*.f32`
32×	`lower-+.f64`
32×	`lower-+.f32`
30×	`lower-fma.f64`
30×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	63
0	24	63
1	35	63
2	42	63
3	45	63
4	47	63
5	51	63
6	76	63
7	90	63
8	91	63
0	91	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize52.0ms (0.4%)

Memory

-15.8MiB live, 94.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (neg.f64 x))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x))))
✓	accuracy	99.7%	(.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))

Samples

17.0ms	129×	0	valid
15.0ms	127×	0	invalid

Compiler

Compiled 49 to 16 computations (67.3% saved)

Precisions

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

ival-mult: 9.0ms (42.3% of total)

ival-sqrt: 6.0ms (28.2% of total)

ival-pow2: 3.0ms (14.1% of total)

ival-div: 2.0ms (9.4% of total)

ival-neg: 1.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

10 → 108

Calls

Call 1

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

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) (patch #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (neg.f64 x)) (patch (sqrt.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (neg.f64 x)) (patch (sqrt.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (neg.f64 x)) (patch (sqrt.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (neg.f64 x)) (patch (sqrt.f64 (neg.f64 x)) #<representation binary64>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (sqrt (* x -2)) (sqrt (neg x)))
0.0ms	x	@	0	(sqrt (* x -2))
0.0ms	x	@	0	(sqrt (neg x))
0.0ms	x	@	inf	(* (sqrt (* x -2)) (sqrt (neg x)))
0.0ms	x	@	-inf	(sqrt (* x -2))

simplify25.0ms (0.2%)

Memory

-9.1MiB live, 32.6MiB allocated

Algorithm

1×	egg-herbie

Rules

164×	`lower-*.f64`
164×	`lower-fma.f64`
164×	`lower-fma.f32`
164×	`lower-*.f32`
108×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	488
1	49	488
2	103	488
3	152	488
4	169	488
5	216	488
6	256	488
7	308	488
8	372	488
9	377	488
0	377	488

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

rewrite276.0ms (2.3%)

Memory

14.2MiB live, 451.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 716×	`lower-*.f32`
4 710×	`lower-*.f64`
3 036×	`lower-fma.f64`
3 036×	`lower-fma.f32`
2 706×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	59
0	24	57
1	61	49
2	196	43
3	999	42
0	9453	42

Stop Event

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

Counts

10 → 1 615

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(+.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 0 binary64)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)))))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 #s(literal 2 binary64) (*.f64 x x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 4 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 2 binary64) (*.f64 x x))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 x #s(literal -2 binary64))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -2 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal -2 binary64) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -2 binary64) (pow.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -2 binary64) (pow.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal -2 binary64) (.f64 (.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -2 binary64) (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 x #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 x #s(literal -2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (pow.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (pow.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 #s(literal 2 binary64) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) x) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
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(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) x #s(literal 0 binary64))
(fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 (neg.f64 (*.f64 x (sqrt.f64 x))) (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(neg.f64 x)
(/.f64 x #s(literal -1 binary64))
(/.f64 (*.f64 x x) (neg.f64 x))
(/.f64 (neg.f64 x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 x (.f64 x x))) (*.f64 x x))
(/.f64 (neg.f64 (*.f64 x x)) x)
(/.f64 (.f64 x (.f64 x x)) (neg.f64 (*.f64 x x)))
(/.f64 (exp.f64 (log.f64 (neg.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/.f64 (exp.f64 (log.f64 (neg.f64 (*.f64 x x)))) x)
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (.f64 (neg.f64 (.f64 x x)) #s(literal 1 binary64)) x)
(/.f64 (.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x x)))
(/.f64 (.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x x)))
(/.f64 (.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) x))
(/.f64 (.f64 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))
(/.f64 (.f64 (neg.f64 (.f64 x (.f64 x x))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (fma.f64 (.f64 x x) (neg.f64 x) #s(literal 0 binary64)) (.f64 x x))
(pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal -1 binary64))
(*.f64 x (exp.f64 (log.f64 #s(literal -1 binary64))))
(.f64 x (.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 x x) (/.f64 #s(literal -1 binary64) x))
(.f64 (neg.f64 x) (.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 1 binary64) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 x) (/.f64 (neg.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 (neg.f64 (*.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) x)))
(.f64 (neg.f64 (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (neg.f64 (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 x x))))
(*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) x)
(.f64 (/.f64 (.f64 x x) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 x)) (/.f64 (neg.f64 (.f64 x (sqrt.f64 x))) (sqrt.f64 x)))
(.f64 (.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (neg.f64 x))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sqrt.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 (neg.f64 x)) #s(literal 1/4 binary64) (*.f64 (log.f64 (neg.f64 x)) #s(literal 1/4 binary64))))
(fabs.f64 (sqrt.f64 x))
(fabs.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(sqrt.f64 (neg.f64 x))
(/.f64 x (sqrt.f64 x))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (sqrt.f64 (neg.f64 (.f64 x (.f64 x x))))))
(/.f64 (*.f64 x (sqrt.f64 x)) x)
(/.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x x)))) x)
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x x))))) (neg.f64 x))
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (neg.f64 x)))
(*.f64 x (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (.f64 (sqrt.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 #s(literal -1 binary64))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))
(.f64 (sqrt.f64 (neg.f64 (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (pow.f64 (neg.f64 x) #s(literal 1/8 binary64)) (.f64 (pow.f64 (neg.f64 x) #s(literal 1/8 binary64)) (sqrt.f64 (sqrt.f64 x))))
(.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (pow.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1/2 binary64)) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (sqrt.f64 x))) (/.f64 x (sqrt.f64 (sqrt.f64 x))))
(.f64 (/.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
(.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (pow.f64 (neg.f64 x) #s(literal 1/8 binary64))) (pow.f64 (neg.f64 x) #s(literal 1/8 binary64)))

eval216.0ms (1.8%)

Memory: 11.1MiB live, 352.5MiB allocated
Compiler: Compiled 24 352 to 2 351 computations (90.3% saved)

prune160.0ms (1.4%)

Memory

-29.7MiB live, 317.3MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	1 723	0	1 723
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	1 723	8	1 731

Accuracy

100.0%

Counts

1 731 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.1%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
✓	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
✓	50.1%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x))))
✓	49.4%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	51.2%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 141 to 71 computations (49.6% saved)

regimes18.0ms (0.2%)

Memory

-4.4MiB live, 33.9MiB allocated

Counts

12 → 2

Calls

Call 1

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

Outputs

#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 (*.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x))))

#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))

Calls

4 calls:

4.0ms	x
4.0ms	(pow.f64 x #s(literal 2 binary64))
4.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
4.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.5%	2	`x`
78.2%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
78.2%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
78.2%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0%)

Memory

7.6MiB live, 7.6MiB allocated

Counts

9 → 2

Calls

Call 1

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

Outputs

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

#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

8 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Memory

-22.3MiB live, 16.3MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Outputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Calls

4 calls:

3.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms	x
2.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
50.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
50.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
50.5%	1	`(pow.f64 x #s(literal 2 binary64))`
52.3%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes6.0ms (0%)

Memory

13.9MiB live, 13.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))

Outputs
(sqrt.f64 #s(literal 2 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
5.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.4%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.4%	1	`(pow.f64 x #s(literal 2 binary64))`
5.4%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch12.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Samples

6.0ms

144×

valid

Compiler

Compiled 199 to 144 computations (27.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (54.6% of total)

ival-mult: 1.0ms (27.3% of total)

ival-sqrt: 1.0ms (27.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Compiler

Compiled 181 to 135 computations (25.4% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Compiler

Compiled 172 to 126 computations (26.7% saved)

bsearch3.0ms (0%)

Memory

-36.9MiB live, 1.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Compiler

Compiled 163 to 117 computations (28.2% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Compiler

Compiled 145 to 108 computations (25.5% saved)

bsearch11.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	-8.949495213371203e-204	-1.9184710424149945e-206

Samples

5.0ms

128×

valid

Compiler

Compiled 98 to 81 computations (17.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 1.0ms (31.9% of total)

ival-sqrt: 1.0ms (31.9% of total)

ival-pow2: 1.0ms (31.9% of total)

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	169
1	50	169
2	59	169
3	63	169
4	64	169

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal -2 binary64))) (sqrt.f64 (neg.f64 x)))) #s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

soundness7.5s (63%)

Memory

-11.5MiB live, 342.5MiB allocated

Rules

3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`
2 986×	`lower-*.f64`
2 908×	`lower-*.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	131
0	39	123
1	101	101
2	354	96
3	1825	90
0	8611	90
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4
0	14	63
0	20	67
1	47	59
2	115	59
3	502	59
4	4969	57
0	8327	57

Stop Event

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

Compiler

Compiled 203 to 105 computations (48.3% saved)

preprocess80.0ms (0.7%)

Memory: 1.0MiB live, 76.4MiB allocated
Compiler: Compiled 222 to 64 computations (71.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	23	488
1	49	488
2	103	488
3	152	488
4	169	488
5	216	488
6	256	488
7	308	488
8	372	488
9	377	488
0	377	488

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	23	488
1	49	488
2	103	488
3	152	488
4	169	488
5	216	488
6	256	488
7	308	488
8	372	488
9	377	488
0	377	488

analyze0.0ms (0%)

sample700.0ms (5.9%)

preprocess18.0ms (0.2%)

explain63.0ms (0.5%)

eval0.0ms (0%)

prune32.0ms (0.3%)

simplify4.0ms (0%)

localize19.0ms (0.2%)

series3.0ms (0%)

simplify36.0ms (0.3%)

rewrite141.0ms (1.2%)

eval18.0ms (0.1%)

prune9.0ms (0.1%)

simplify9.0ms (0.1%)

localize40.0ms (0.3%)

series3.0ms (0%)

simplify8.0ms (0.1%)

rewrite313.0ms (2.6%)

eval441.0ms (3.7%)

prune236.0ms (2%)

simplify46.0ms (0.4%)

localize84.0ms (0.7%)

series17.0ms (0.1%)

simplify273.0ms (2.3%)

rewrite273.0ms (2.3%)

eval470.0ms (4%)

prune234.0ms (2%)

simplify7.0ms (0.1%)

localize52.0ms (0.4%)

series5.0ms (0%)

simplify25.0ms (0.2%)

rewrite276.0ms (2.3%)

eval216.0ms (1.8%)

prune160.0ms (1.4%)

regimes18.0ms (0.2%)

regimes4.0ms (0%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

bsearch12.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch3.0ms (0%)

bsearch1.0ms (0%)

bsearch11.0ms (0.1%)

simplify8.0ms (0.1%)

soundness7.5s (63%)

preprocess80.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	23	488
1	49	488
2	103	488
3	152	488
4	169	488
5	216	488
6	256	488
7	308	488
8	372	488
9	377	488
0	377	488