Metrics for sqrt D (should all be same)

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample833.0ms (7.1%)

Memory

8.0MiB live, 753.3MiB allocated

Samples

642.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 282.0ms

ival-pow2: 161.0ms (57% of total)

ival-sqrt: 55.0ms (19.5% of total)

ival-mult: 54.0ms (19.1% of total)

ival-true: 5.0ms (1.8% of total)

exact: 5.0ms (1.8% of total)

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

Bogosity

preprocess18.0ms (0.2%)

Memory

-9.3MiB live, 28.7MiB 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)))

explain70.0ms (0.6%)

Memory

0.7MiB live, 124.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
126	-	2	(-1.4262373922273299e-161)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	72	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	73
↳	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	overflow	1
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	73
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	52	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	52
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	52

Confusion

	Predicted +	Predicted -
+	124	2
-	0	130

Precision

1.0

Recall

0.9841269841269841

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	2
-	0	0	130

Precision?

1.0

Recall?

0.9841269841269841

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-pow2: 15.0ms (66.7% of total)

ival-mult: 3.0ms (13.3% of total)

ival-sqrt: 3.0ms (13.3% 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

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.4%	(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

2.5MiB live, 2.5MiB 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

localize18.0ms (0.2%)

Memory

14.0MiB live, 14.0MiB 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	54.5%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow2: 3.0ms (49.6% of total)

ival-sqrt: 2.0ms (33.1% of total)

ival-mult: 1.0ms (16.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

2.0MiB live, 2.0MiB 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	(pow x 2)
0.0ms	x	@	inf	(sqrt (* 2 (pow x 2)))
0.0ms	x	@	0	(pow x 2)

simplify74.0ms (0.6%)

Memory

-33.7MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite151.0ms (1.3%)

Memory

35.7MiB live, 189.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

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

Counts

3 → 46

Calls

Call 1

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

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

eval18.0ms (0.2%)

Memory: -28.0MiB live, 22.9MiB allocated
Compiler: Compiled 599 to 120 computations (80% saved)

prune7.0ms (0.1%)

Memory

14.0MiB live, 14.0MiB 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
▶	54.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
▶	5.5%	(sqrt.f64 #s(literal 2 binary64))
▶	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	50.7%	#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)

simplify11.0ms (0.1%)

Memory

-23.3MiB live, 13.0MiB 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

localize41.0ms (0.3%)

Memory

15.2MiB live, 92.9MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	#s(approx (pow x 2) (*.f64 x x))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
✓	accuracy	54.5%	(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	99.4%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.1%	#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	99.4%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Samples

23.0ms

256×

valid

Compiler

Compiled 57 to 11 computations (80.7% saved)

Precisions

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

ival-mult: 5.0ms (38.4% of total)

ival-sqrt: 4.0ms (30.7% of total)

ival-pow2: 3.0ms (23.1% of total)

ival-neg: 1.0ms (7.7% 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

3.7MiB live, 3.7MiB 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	@	-inf	(* x (sqrt 2))
0.0ms	x	@	0	(sqrt (* 2 (pow x 2)))

simplify8.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB 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)

rewrite291.0ms (2.5%)

Memory

1.5MiB live, 397.7MiB 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)))
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(.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(approx (pow x 2) (*.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (*.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(approx (pow x 2) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/8 binary64)))
(.f64 (.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (pow x 2) (.f64 x x)))) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
(.f64 #s(literal 2 binary64) (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 2 binary64))
(.f64 (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))) #s(literal 2 binary64))
#s(approx (pow x 2) (*.f64 x x))
(+.f64 (*.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(fabs.f64 (neg.f64 (*.f64 x x)))
(fabs.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 x (.f64 x (*.f64 x x))))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 0 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 0 binary64)) (-.f64 (.f64 x x) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 8 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))))

eval215.0ms (1.8%)

Memory: -2.3MiB live, 453.1MiB allocated
Compiler: Compiled 30 881 to 1 701 computations (94.5% saved)

prune178.0ms (1.5%)

Memory

-5.9MiB live, 376.5MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	1 832	6	1 838
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 832	10	1 842

Accuracy

100.0%

Counts

1 842 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.5%	(sqrt.f64 #s(literal 2 binary64))
▶	50.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
▶	50.6%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
▶	49.7%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
	50.3%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 148 to 99 computations (33.1% saved)

simplify63.0ms (0.5%)

Memory

14.1MiB live, 52.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	128	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 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 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
✓	cost-diff	1408	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Rules

420×	`lower-*.f32`
416×	`lower-fma.f64`
416×	`lower-fma.f32`
410×	`lower-*.f64`
330×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	159
0	38	155
1	60	149
2	97	149
3	163	149
4	343	149
5	662	149
6	1180	149
7	1337	149
8	1349	149
9	1358	149
10	1358	149
0	1358	149

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize85.0ms (0.7%)

Memory

-18.2MiB live, 177.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	accuracy	99.7%	(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.7%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	51.0%	#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	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	accuracy	99.7%	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	accuracy	99.2%	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
✓	accuracy	99.8%	(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.8%	(/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

Samples

23.0ms	128×	0	valid
23.0ms	128×	0	invalid

Compiler

Compiled 122 to 22 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 11.0ms (38.9% of total)

ival-div: 6.0ms (21.2% of total)

ival-sqrt: 6.0ms (21.2% of total)

ival-pow2: 3.0ms (10.6% of total)

ival-neg: 1.0ms (3.5% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

18 → 192

Calls

Call 1

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

Calls

48 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* (/ 2 (sqrt 2)) x)
1.0ms	x	@	-inf	(* (sqrt (* 2 x)) (sqrt x))
1.0ms	x	@	inf	(/ -1 (* x (sqrt 2)))
0.0ms	x	@	-inf	(* (/ 2 (sqrt 2)) x)
0.0ms	x	@	inf	(neg (/ (* x -2) (sqrt 2)))

simplify273.0ms (2.3%)

Memory

-8.9MiB live, 263.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	880
1	58	880
2	148	880
3	277	880
4	509	880
5	824	880
6	1379	880
7	1510	880
8	1634	880
9	1855	880
10	2093	880
11	2545	880
12	2621	880
13	2647	880
14	2651	880
15	2651	880
16	2651	880
17	2688	880
18	3492	880
19	4429	880
20	5328	880
21	5696	880
22	5898	880
23	5942	880
24	7073	880
25	7597	880
26	7752	880
0	8064	880

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

rewrite246.0ms (2.1%)

Memory

12.5MiB live, 385.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 716×	`lower-*.f32`
2 706×	`lower-*.f64`
1 940×	`lower-fma.f64`
1 940×	`lower-fma.f32`
1 780×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	131
0	38	127
1	99	95
2	345	91
3	1735	90
0	8179	90

Stop Event

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

Counts

18 → 2 577

Calls

Call 1

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

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

eval467.0ms (4%)

Memory: 35.0MiB live, 628.8MiB allocated
Compiler: Compiled 42 822 to 3 321 computations (92.2% saved)

prune492.0ms (4.2%)

Memory

-50.5MiB live, 496.2MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	3 363	3	3 366
Fresh	1	0	1
Picked	3	2	5
Done	0	4	4
Total	3 367	9	3 376

Accuracy

100.0%

Counts

3 376 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.5%	(sqrt.f64 #s(literal 2 binary64))
▶	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	50.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
▶	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
✓	49.7%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 65 to 45 computations (30.8% saved)

simplify6.0ms (0%)

Memory

6.9MiB live, 6.9MiB 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	(/.f64 #s(literal -1 binary64) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
✓	cost-diff	384	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
✓	cost-diff	384	(/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Rules

34×	`lower-*.f32`
32×	`lower-*.f64`
20×	`lower-/.f32`
12×	`*-commutative`
10×	`lift-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	80
0	23	80
1	31	80
2	38	80
3	43	80
4	44	80
0	44	80

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize49.0ms (0.4%)

Memory

27.2MiB live, 101.7MiB 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	51.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal -1 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))
✓	accuracy	51.0%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	accuracy	99.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	accuracy	51.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Samples

27.0ms

256×

valid

Compiler

Compiled 61 to 15 computations (75.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-div: 8.0ms (45.5% of total)

ival-mult: 3.0ms (17.1% of total)

ival-sqrt: 3.0ms (17.1% of total)

ival-pow2: 3.0ms (17.1% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

27 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ -1 x)
0.0ms	x	@	-inf	(/ (sqrt 2) x)
0.0ms	x	@	inf	(/ -1 x)
0.0ms	x	@	0	(/ 2 (/ (sqrt 2) x))
0.0ms	x	@	inf	(/ 2 (/ (sqrt 2) x))

simplify15.0ms (0.1%)

Memory

-24.7MiB live, 14.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	480
1	19	480
2	34	480
3	39	480
4	43	480
5	55	480
6	67	480
7	78	480
8	101	480
9	115	480
10	117	480
0	117	480

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

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

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

rewrite227.0ms (1.9%)

Memory

32.6MiB live, 428.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 420×	`lower-*.f32`
2 418×	`lower-*.f64`
1 764×	`lower-/.f32`
1 754×	`lower-/.f64`
1 608×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	69
0	23	69
1	75	63
2	295	63
3	1240	51
4	7043	51
0	8681	51

Stop Event

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

Counts

10 → 1 108

Calls

Call 1

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

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

eval190.0ms (1.6%)

Memory: -10.4MiB live, 287.9MiB allocated
Compiler: Compiled 16 872 to 1 705 computations (89.9% saved)

prune106.0ms (0.9%)

Memory

31.2MiB live, 226.9MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	1 362	0	1 362
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	1 362	9	1 371

Accuracy

100.0%

Counts

1 371 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.4%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.5%	(sqrt.f64 #s(literal 2 binary64))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	50.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
✓	49.7%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
✓	50.8%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	50.7%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 169 to 81 computations (52.1% saved)

regimes33.0ms (0.3%)

Memory

-54.0MiB live, 26.2MiB allocated

Counts

14 → 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)))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

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

Calls

4 calls:

19.0ms	(pow.f64 x #s(literal 2 binary64))
5.0ms	x
4.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
4.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
76.5%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
76.5%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
76.5%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes5.0ms (0%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

10 → 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)))))
#s(approx (sqrt (* 2 (pow x 2))) (.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)) (sqrt.f64 x)))
#s(approx (sqrt (* 2 (pow x 2))) (/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0.1%)

Memory

-21.3MiB live, 16.6MiB 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:

4.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms	x
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
2.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
50.8%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
50.8%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
50.8%	1	`(pow.f64 x #s(literal 2 binary64))`
52.6%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes5.0ms (0%)

Memory

13.6MiB live, 13.6MiB 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
5.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.5%	1	`(pow.f64 x #s(literal 2 binary64))`
5.5%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch11.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	-1.0888264154076973e-305	4.1858451350630773e-308

Samples

5.0ms

128×

valid

Compiler

Compiled 138 to 105 computations (23.9% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.0888264154076973e-305	4.1858451350630773e-308

Compiler

Compiled 130 to 97 computations (25.4% saved)

bsearch177.0ms (1.5%)

Memory

-19.0MiB live, 19.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
176.0ms	-3.041784631888261e-205	-7.187918551088748e-215

Samples

171.0ms

144×

valid

Compiler

Compiled 109 to 90 computations (17.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-mult: 165.0ms (98.2% of total)

ival-pow2: 2.0ms (1.2% of total)

ival-sqrt: 1.0ms (0.6% 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

12.2MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-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	21	74
1	29	74
2	38	74
3	43	74
4	45	74

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) x))) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

soundness7.3s (62%)

Memory

-18.6MiB live, 294.8MiB allocated

Rules

3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`
2 986×	`lower-*.f64`
2 716×	`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	25	131
0	38	127
1	99	95
2	345	91
3	1735	90
0	8179	90
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 72 to 37 computations (48.6% saved)

preprocess31.0ms (0.3%)

Memory: 39.2MiB live, 77.2MiB allocated
Compiler: Compiled 104 to 40 computations (61.5% 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	11	480
1	19	480
2	34	480
3	39	480
4	43	480
5	55	480
6	67	480
7	78	480
8	101	480
9	115	480
10	117	480
0	117	480

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	11	480
1	19	480
2	34	480
3	39	480
4	43	480
5	55	480
6	67	480
7	78	480
8	101	480
9	115	480
10	117	480
0	117	480

analyze0.0ms (0%)

sample833.0ms (7.1%)

preprocess18.0ms (0.2%)

explain70.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize18.0ms (0.2%)

series3.0ms (0%)

simplify74.0ms (0.6%)

rewrite151.0ms (1.3%)

eval18.0ms (0.2%)

prune7.0ms (0.1%)

simplify11.0ms (0.1%)

localize41.0ms (0.3%)

series1.0ms (0%)

simplify8.0ms (0.1%)

rewrite291.0ms (2.5%)

eval215.0ms (1.8%)

prune178.0ms (1.5%)

simplify63.0ms (0.5%)

localize85.0ms (0.7%)

series9.0ms (0.1%)

simplify273.0ms (2.3%)

rewrite246.0ms (2.1%)

eval467.0ms (4%)

prune492.0ms (4.2%)

simplify6.0ms (0%)

localize49.0ms (0.4%)

series4.0ms (0%)

simplify15.0ms (0.1%)

rewrite227.0ms (1.9%)

eval190.0ms (1.6%)

prune106.0ms (0.9%)

regimes33.0ms (0.3%)

regimes5.0ms (0%)

regimes9.0ms (0.1%)

regimes5.0ms (0%)

bsearch11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch177.0ms (1.5%)

simplify7.0ms (0.1%)

soundness7.3s (62%)

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	11	480
1	19	480
2	34	480
3	39	480
4	43	480
5	55	480
6	67	480
7	78	480
8	101	480
9	115	480
10	117	480
0	117	480