Metrics for sqrt D (should all be same)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample986.0ms (9.3%)

Memory

21.2MiB live, 735.9MiB allocated

Samples

696.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 378.0ms

ival-pow2: 248.0ms (65.7% of total)

ival-sqrt: 62.0ms (16.4% of total)

ival-mult: 54.0ms (14.3% of total)

ival-true: 5.0ms (1.3% of total)

exact: 5.0ms (1.3% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

preprocess19.0ms (0.2%)

Memory

-9.1MiB live, 29.7MiB 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)))

explain60.0ms (0.6%)

Memory

21.9MiB live, 99.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
119	-	-	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
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))))`	oflow-rescue	61	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	61
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	61
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	58	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	58
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	58

Confusion

	Predicted +	Predicted -
+	119	0
-	0	137

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	119	0	0
-	0	0	137

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	137
1	119

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

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

ival-pow2: 7.0ms (49.9% of total)

ival-mult: 3.0ms (21.4% of total)

ival-sqrt: 3.0ms (21.4% 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.6%	(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

6.5MiB live, 6.5MiB 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

localize22.0ms (0.2%)

Memory

-9.3MiB live, 33.9MiB 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	56.6%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

16.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow2: 6.0ms (59.2% of total)

ival-mult: 2.0ms (19.7% of total)

ival-sqrt: 2.0ms (19.7% 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

3.0MiB live, 3.0MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>

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	(sqrt (* 2 (pow x 2)))
0.0ms	x	@	inf	(pow x 2)
0.0ms	x	@	0	(pow x 2)

simplify10.0ms (0.1%)

Memory

-30.2MiB live, 8.4MiB 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)))

rewrite241.0ms (2.3%)

Memory

2.1MiB live, 197.3MiB 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)

eval8.0ms (0.1%)

Memory: 20.1MiB live, 20.1MiB allocated
Compiler: Compiled 599 to 120 computations (80% saved)

prune7.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB 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
▶	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
▶	5.4%	(sqrt.f64 #s(literal 2 binary64))
▶	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	53.0%	#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)

simplify10.0ms (0.1%)

Memory

-26.2MiB live, 10.6MiB 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

localize44.0ms (0.4%)

Memory

10.0MiB live, 61.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
✓	accuracy	100.0%	#s(approx (pow x 2) (*.f64 x x))
✓	accuracy	56.6%	(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	48.8%	#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	53.4%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Samples

26.0ms

256×

valid

Compiler

Compiled 57 to 11 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 9.0ms (53.9% of total)

ival-sqrt: 3.0ms (18% of total)

ival-pow2: 3.0ms (18% of total)

ival-neg: 1.0ms (6% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

9 → 96

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

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	@	-inf	(* x (sqrt 2))

simplify10.0ms (0.1%)

Memory

-25.5MiB live, 13.3MiB 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)

rewrite252.0ms (2.4%)

Memory

13.5MiB live, 366.3MiB 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)))
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(.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))))

eval220.0ms (2.1%)

Memory: 25.1MiB live, 445.7MiB allocated
Compiler: Compiled 30 881 to 1 701 computations (94.5% saved)

prune163.0ms (1.5%)

Memory

5.8MiB live, 399.4MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 835	3	1 838
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 835	7	1 842

Accuracy

100.0%

Counts

1 842 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
▶	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	48.3%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	48.5%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 49 to 35 computations (28.6% saved)

simplify70.0ms (0.7%)

Memory

-41.3MiB live, 25.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	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))))
✓	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	(*.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))))

Rules

130×	`lower-fma.f64`
130×	`lower-fma.f32`
130×	`lower-*.f32`
126×	`lower-*.f64`
72×	`lower-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	89
0	21	91
1	37	87
2	64	87
3	112	87
4	149	87
5	186	87
6	223	87
7	257	87
8	285	87
9	289	87
0	289	87

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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 (/.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))) (/.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)

Outputs
#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 (/.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))) (/.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)

localize55.0ms (0.5%)

Memory

28.7MiB live, 106.4MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal -2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	53.4%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	accuracy	98.4%	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	48.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) 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	99.3%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	48.8%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Samples

26.0ms

256×

valid

Compiler

Compiled 69 to 14 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 4.0ms (24.5% of total)

ival-pow2: 4.0ms (24.5% of total)

ival-div: 3.0ms (18.3% of total)

ival-sqrt: 3.0ms (18.3% of total)

ival-neg: 1.0ms (6.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

-27.5MiB live, 11.2MiB allocated

Counts

9 → 84

Calls

Call 1

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

Outputs
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 (/ x (sqrt 2)))>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* -2 x)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* x -2)
1.0ms	x	@	inf	(/ (* x -2) (sqrt 2))
1.0ms	x	@	0	(neg (/ (* x -2) (sqrt 2)))
0.0ms	x	@	inf	(neg (/ (* x -2) (sqrt 2)))
0.0ms	x	@	-inf	(/ (* x -2) (sqrt 2))

simplify9.0ms (0.1%)

Memory

18.1MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Rules

48×	`lower-*.f64`
48×	`lower-fma.f64`
48×	`lower-fma.f32`
48×	`lower-*.f32`
44×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	408
1	22	408
2	39	408
3	46	408
4	51	408
5	63	408
6	75	408
7	86	408
8	114	408
9	126	408
10	127	408
0	127	408

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

Inputs
(* 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)))
(* -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)))
(* 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)))

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

rewrite229.0ms (2.2%)

Memory

20.2MiB live, 372.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 632×	`lower-*.f32`
3 628×	`lower-*.f64`
2 426×	`lower-/.f32`
2 422×	`lower-/.f64`
1 860×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	68
0	21	74
1	59	62
2	207	46
3	1253	46
0	8586	46

Stop Event

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

Counts

9 → 1 869

Calls

Call 1

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

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

eval343.0ms (3.2%)

Memory: 20.3MiB live, 515.9MiB allocated
Compiler: Compiled 36 072 to 2 115 computations (94.1% saved)

prune230.0ms (2.2%)

Memory

-3.0MiB live, 405.8MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	2 754	1	2 755
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	2 756	6	2 762

Accuracy

100.0%

Counts

2 762 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
▶	48.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 40 to 28 computations (30% saved)

simplify10.0ms (0.1%)

Memory

-36.1MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

22×	`lower-*.f32`
20×	`lower-*.f64`
8×	`*-commutative`
6×	`lower-/.f32`
4×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
0	12	26
1	17	26
2	22	26
3	23	26
0	23	26

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))

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

localize27.0ms (0.3%)

Memory

12.3MiB live, 49.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	48.8%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Samples

19.0ms

256×

valid

Compiler

Compiled 21 to 10 computations (52.4% saved)

Precisions

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

ival-pow2: 4.0ms (31.4% of total)

ival-mult: 3.0ms (23.6% of total)

ival-sqrt: 3.0ms (23.6% of total)

ival-div: 2.0ms (15.7% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Counts

4 → 36

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 (/ x (sqrt 2)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>

Calls

9 calls:

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

simplify7.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	160
1	17	160
2	32	160
3	37	160
4	41	160
5	53	160
6	65	160
7	76	160
8	97	160
9	106	160
10	107	160
0	107	160

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

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)

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

rewrite173.0ms (1.6%)

Memory

5.8MiB live, 197.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 718×	`lower-*.f32`
2 716×	`lower-*.f64`
1 456×	`lower-/.f32`
1 454×	`lower-/.f64`
848×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	24
0	12	24
1	36	20
2	128	20
3	616	18
0	4771	18

Stop Event

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

Counts

4 → 355

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))

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

eval48.0ms (0.5%)

Memory: 12.4MiB live, 87.9MiB allocated
Compiler: Compiled 4 758 to 775 computations (83.7% saved)

prune320.0ms (3%)

Memory

-54.3MiB live, 131.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	391	6	397

Accuracy

100.0%

Counts

397 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.4%	(sqrt.f64 #s(literal 2 binary64))
✓	48.5%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	53.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 96 to 47 computations (51% saved)

regimes14.0ms (0.1%)

Memory

33.2MiB live, 33.2MiB 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 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))))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (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))) (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))))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.4%	2	`x`
78.9%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
78.9%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
78.9%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0%)

Memory

-31.1MiB live, 8.2MiB 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 x #s(literal -2 binary64)) (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 x (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB 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:

2.0ms	x
2.0ms	(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
48.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
48.4%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
48.4%	1	`(pow.f64 x #s(literal 2 binary64))`
50.3%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes5.0ms (0%)

Memory

15.1MiB live, 15.1MiB 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	(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)))
1.0ms	(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)

bsearch16.0ms (0.1%)

Memory

-5.5MiB live, 33.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-5.893621989568688e-302	1.2791351447617957e-284

Samples

8.0ms

176×

valid

Compiler

Compiled 197 to 141 computations (28.4% saved)

Precisions

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

ival-pow2: 2.0ms (46.3% of total)

ival-mult: 1.0ms (23.2% of total)

ival-sqrt: 1.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-5.893621989568688e-302	1.2791351447617957e-284

Compiler

Compiled 175 to 130 computations (25.7% saved)

bsearch15.0ms (0.1%)

Memory

-8.1MiB live, 30.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-1.2252824571745956e-191	-1.4554021955138073e-206

Samples

7.0ms

160×

valid

Compiler

Compiled 120 to 99 computations (17.5% saved)

Precisions

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

ival-pow2: 2.0ms (51.7% of total)

ival-mult: 1.0ms (25.8% of total)

ival-sqrt: 1.0ms (25.8% of total)

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

exact: 0.0ms (0% of total)

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

simplify7.0ms (0.1%)

Memory

17.7MiB live, 17.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-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	20	75
1	30	75
2	39	75
3	44	75
4	46	75

Stop Event

1×

saturated

Calls

Call 1

Inputs
(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))

Outputs
(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))

soundness6.9s (65.2%)

Memory

7.1MiB live, 350.2MiB allocated

Rules

3 632×	`lower-*.f32`
3 628×	`lower-*.f64`
3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`

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
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	15	68
0	21	74
1	59	62
2	207	46
3	1253	46
0	8586	46
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×	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 90 to 49 computations (45.6% saved)

preprocess31.0ms (0.3%)

Memory: -14.1MiB live, 60.4MiB allocated
Compiler: Compiled 106 to 38 computations (64.2% 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	15	89
0	21	91
1	37	87
2	64	87
3	112	87
4	149	87
5	186	87
6	223	87
7	257	87
8	285	87
9	289	87
0	289	87

Iter	Nodes	Cost
0	11	408
1	22	408
2	39	408
3	46	408
4	51	408
5	63	408
6	75	408
7	86	408
8	114	408
9	126	408
10	127	408
0	127	408

Iter	Nodes	Cost
0	9	160
1	17	160
2	32	160
3	37	160
4	41	160
5	53	160
6	65	160
7	76	160
8	97	160
9	106	160
10	107	160
0	107	160

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	15	89
0	21	91
1	37	87
2	64	87
3	112	87
4	149	87
5	186	87
6	223	87
7	257	87
8	285	87
9	289	87
0	289	87

Iter	Nodes	Cost
0	11	408
1	22	408
2	39	408
3	46	408
4	51	408
5	63	408
6	75	408
7	86	408
8	114	408
9	126	408
10	127	408
0	127	408

Iter	Nodes	Cost
0	9	160
1	17	160
2	32	160
3	37	160
4	41	160
5	53	160
6	65	160
7	76	160
8	97	160
9	106	160
10	107	160
0	107	160

analyze0.0ms (0%)

sample986.0ms (9.3%)

preprocess19.0ms (0.2%)

explain60.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize22.0ms (0.2%)

series3.0ms (0%)

simplify10.0ms (0.1%)

rewrite241.0ms (2.3%)

eval8.0ms (0.1%)

prune7.0ms (0.1%)

simplify10.0ms (0.1%)

localize44.0ms (0.4%)

series2.0ms (0%)

simplify10.0ms (0.1%)

rewrite252.0ms (2.4%)

eval220.0ms (2.1%)

prune163.0ms (1.5%)

simplify70.0ms (0.7%)

localize55.0ms (0.5%)

series6.0ms (0.1%)

simplify9.0ms (0.1%)

rewrite229.0ms (2.2%)

eval343.0ms (3.2%)

prune230.0ms (2.2%)

simplify10.0ms (0.1%)

localize27.0ms (0.3%)

series1.0ms (0%)

simplify7.0ms (0.1%)

rewrite173.0ms (1.6%)

eval48.0ms (0.5%)

prune320.0ms (3%)

regimes14.0ms (0.1%)

regimes4.0ms (0%)

regimes6.0ms (0.1%)

regimes5.0ms (0%)

bsearch16.0ms (0.1%)

bsearch1.0ms (0%)

bsearch15.0ms (0.1%)

simplify7.0ms (0.1%)

soundness6.9s (65.2%)

preprocess31.0ms (0.3%)

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	15	89
0	21	91
1	37	87
2	64	87
3	112	87
4	149	87
5	186	87
6	223	87
7	257	87
8	285	87
9	289	87
0	289	87

Iter	Nodes	Cost
0	11	408
1	22	408
2	39	408
3	46	408
4	51	408
5	63	408
6	75	408
7	86	408
8	114	408
9	126	408
10	127	408
0	127	408

Iter	Nodes	Cost
0	9	160
1	17	160
2	32	160
3	37	160
4	41	160
5	53	160
6	65	160
7	76	160
8	97	160
9	106	160
10	107	160
0	107	160