Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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 10 to 6 computations (40% saved)

sample566.0ms (16.5%)

Memory

33.2MiB live, 772.3MiB allocated

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-pow2: 95.0ms (48.1% of total)

ival-sqrt: 56.0ms (28.3% of total)

ival-add: 39.0ms (19.7% of total)

ival-true: 5.0ms (2.5% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain69.0ms (2%)

Memory

-26.6MiB live, 95.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
123	0	-	2	(-1.1253006180688229e-161)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	68	(-2.0388297132282653e+266)	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	nan-rescue	68	0
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	68
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	68
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	68	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	68
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	136
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	53	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	53
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	106

Confusion

	Predicted +	Predicted -
+	121	2
-	0	133

Precision

1.0

Recall

0.983739837398374

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	2
-	0	0	133

Precision?

1.0

Recall?

0.983739837398374

Freqs

test

number	freq
0	135
1	53
2	68

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 74 to 34 computations (54.1% saved)

Precisions

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

ival-pow2: 9.0ms (52.3% of total)

ival-add: 4.0ms (23.2% of total)

ival-sqrt: 4.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess18.0ms (0.5%)

Memory

24.1MiB live, 24.1MiB allocated

Algorithm

1×	egg-herbie

Rules

58×	`associate-r`
54×	`unsub-neg`
38×	`distribute-rgt-neg-out`
38×	`distribute-lft-neg-out`
38×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.5%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify8.0ms (0.2%)

Memory

-31.9MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
cost-diff	320	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Rules

14×	`lower-*.f64`
14×	`lower-*.f32`
4×	`*-commutative`
4×	`count-2`
4×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	20
0	8	16
1	10	16
2	15	16
3	18	16
0	18	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.5%)

Memory

25.1MiB live, 25.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(pow.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
accuracy	28.50035930158269	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

11.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

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

ival-pow2: 3.0ms (49.3% of total)

ival-sqrt: 2.0ms (32.9% of total)

ival-add: 1.0ms (16.4% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

#<alt (sqrt.f64 (+.f64 (pow.f64 x #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 (* 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 (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>

Calls

9 calls:

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

simplify9.0ms (0.3%)

Memory

-29.5MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	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)
(* 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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))

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

rewrite38.0ms (1.1%)

Memory

7.3MiB live, 45.0MiB allocated

Rules

70×	`lower-*.f64`
70×	`lower-*.f32`
44×	`lower-fma.f64`
44×	`lower-fma.f32`
34×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	18
0	8	14
1	28	10
0	170	9

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

3 → 33

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: 14.5MiB live, 14.5MiB allocated
Compiler: Compiled 774 to 104 computations (86.6% saved)

prune8.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Accuracy

100.0%

Counts

88 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	22.1%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
▶	55.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	50.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	50.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 100 to 50 computations (50% saved)

simplify262.0ms (7.6%)

Memory

-11.1MiB live, 144.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
cost-diff	0	(+.f64 x x)
cost-diff	0	(*.f64 x (+.f64 x x))
cost-diff	0	(sqrt.f64 (*.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	5312	(hypot.f64 x x)

Rules

2 560×	`lower-fma.f32`
2 558×	`lower-fma.f64`
1 984×	`lower-*.f32`
1 976×	`lower-*.f64`
1 218×	`unsub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	151
0	36	127
1	56	107
2	118	100
3	220	94
4	308	94
5	583	94
6	629	94
7	701	94
8	746	94
9	897	94
10	1365	94
11	2259	94
12	2955	94
13	3123	94
14	3289	94
15	3321	94
16	3745	94
17	3951	94
18	3957	94
19	3957	94
20	3957	94
21	3957	94
22	3977	94
23	3985	94
24	3985	94
25	3985	94
26	3991	94
0	3991	94

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (+ (pow x 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)
#s(approx (sqrt (+ (pow x 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)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))

Outputs
(hypot.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
x
#s(approx (sqrt (+ (pow x 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)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 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)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x (+.f64 x x))))))) (.f64 x x))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x (+.f64 x x)))))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x (+.f64 x x))))))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(*.f64 x x)

localize82.0ms (2.4%)

Memory

-14.7MiB live, 103.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.966661588848703	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	13.200489485616076	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	37.63075338155759	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 x (+.f64 x x))
accuracy	28.50035930158269	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.40625	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	31.29983926356736	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.40625	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	31.325185081774666	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.015625	(hypot.f64 x x)

Samples

55.0ms

256×

valid

Compiler

Compiled 153 to 22 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-hypot: 8.0ms (25.2% of total)

ival-sqrt: 8.0ms (25.2% of total)

ival-mult: 7.0ms (22.1% of total)

ival-add: 3.0ms (9.5% of total)

ival-div: 2.0ms (6.3% of total)

ival-pow2: 2.0ms (6.3% of total)

ival-neg: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>
#<alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.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 (+ (pow x 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 (sqrt.f64 (*.f64 x (+.f64 x x)))>
#<alt (*.f64 x (+.f64 x x))>
#<alt (+.f64 x x)>
#<alt (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))>
#<alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))>
#<alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))>
#<alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.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 (* 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 (* 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 (* -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 (* 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 (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 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>

Calls

36 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x))))
0.0ms	x	@	inf	(* x (+ x x))
0.0ms	x	@	0	(+ (* (* x x) (* x x)) 0)
0.0ms	x	@	inf	(+ x x)
0.0ms	x	@	0	(+ x x)

simplify15.0ms (0.4%)

Memory

25.1MiB live, 25.1MiB allocated

Algorithm

1×	egg-herbie

Rules

130×	`lower-*.f64`
130×	`lower-fma.f64`
130×	`lower-fma.f32`
130×	`lower-*.f32`
64×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	612
1	30	612
2	65	612
3	113	612
4	132	612
5	173	612
6	207	612
7	236	612
8	273	612
9	278	612
0	278	612

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 144

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* 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))
(* 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))
(* -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))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(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 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 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))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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)))
(* -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 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x 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))
(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 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 x x) (neg.f64 x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 x x) (neg.f64 x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 x x) (neg.f64 x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (*.f64 x x) (neg.f64 x)))

rewrite122.0ms (3.6%)

Memory

-18.5MiB live, 66.7MiB allocated

Rules

180×	`lower-*.f32`
176×	`lower-*.f64`
142×	`lower-fma.f32`
140×	`lower-fma.f64`
104×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	112
0	36	57
1	116	36
0	896	36

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

13 → 71

Calls

Call 1

Inputs
(hypot.f64 x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.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 (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))

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

eval28.0ms (0.8%)

Memory: 13.8MiB live, 52.8MiB allocated
Compiler: Compiled 5 055 to 302 computations (94% saved)

prune19.0ms (0.6%)

Memory

1.8MiB live, 39.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	296	7	303

Accuracy

100.0%

Counts

303 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	23.0%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	55.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	50.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	50.6%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	50.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	3.7%	#s(literal 0 binary64)

Compiler

Compiled 55 to 33 computations (40% saved)

simplify12.0ms (0.3%)

Memory

-19.3MiB live, 19.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

122×	`lower-*.f32`
114×	`lower-fma.f32`
112×	`lower-*.f64`
112×	`lower-fma.f64`
72×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	107
0	31	95
1	52	76
2	112	70
3	197	64
4	227	64
0	227	61

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
x
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(*.f64 x x)
x
#s(literal 0 binary64)
(*.f64 x (+.f64 x x))
(+.f64 x x)

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

localize117.0ms (3.4%)

Memory

11.1MiB live, 93.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.078125	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.17578125	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.966661588848703	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	37.63075338155759	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.40625	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	31.325185081774666	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Samples

100.0ms

256×

valid

Compiler

Compiled 105 to 21 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-div: 58.0ms (65.4% of total)

ival-mult: 14.0ms (15.8% of total)

ival-add: 3.0ms (3.4% of total)

ival-exp: 3.0ms (3.4% of total)

ival-log: 3.0ms (3.4% of total)

ival-sqrt: 3.0ms (3.4% of total)

ival-pow2: 3.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

9 → 72

Calls

Call 1

Inputs
#<alt (exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))>
#<alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))>
#<alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))>
#<alt (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))>
#<alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))>
#<alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))>
#<alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))>
#<alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))>
#<alt (log.f64 #s(literal 2 binary64))>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 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 (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	inf	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	0	(* x (exp (* (log 2) 1/2)))
0.0ms	x	@	-inf	(* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))
0.0ms	x	@	0	(sqrt (+ (pow x 2) (pow x 2)))

simplify16.0ms (0.5%)

Memory

-18.2MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Rules

122×	`lower-*.f64`
122×	`lower-*.f32`
118×	`lower-fma.f64`
118×	`lower-fma.f32`
56×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* x (sqrt 2))
(* 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))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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))))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* (pow x 3) (sqrt 2))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))

rewrite199.0ms (5.8%)

Memory

4.3MiB live, 163.8MiB allocated

Rules

2 890×	`lower-fma.f32`
2 888×	`lower-fma.f64`
1 810×	`lower-*.f32`
1 806×	`lower-*.f64`
936×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	90
0	31	50
1	101	21
2	799	18
3	4978	18
0	8339	18

Stop Event

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

Counts

9 → 133

Calls

Call 1

Inputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
(log.f64 #s(literal 2 binary64))

Outputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.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 1/4 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 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.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 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 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)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))
#s(literal 0 binary64)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 8 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -4 binary64) (log.f64 x)) #s(literal -1 binary64)))
(fabs.f64 (.f64 x (.f64 x (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(sqrt.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) x #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (.f64 (.f64 x x) (*.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 x)) (.f64 x (*.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (/.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (*.f64 x (sqrt.f64 x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (neg.f64 x) (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(neg.f64 (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) x)
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (pow.f64 x #s(literal 36 binary64)) (pow.f64 (*.f64 x x) #s(literal 16 binary64)))
(/.f64 (pow.f64 x #s(literal 24 binary64)) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))))
(/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(/.f64 (pow.f64 (*.f64 x x) #s(literal 14 binary64)) (pow.f64 x #s(literal 24 binary64)))
(/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 1 binary64)) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (*.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 8 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal 2 binary64)) (exp.f64 #s(literal 2 binary64))) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 x))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 (.f64 x (*.f64 x x)) (neg.f64 x))
(.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 x (.f64 x (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (sqrt.f64 x) (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))))
(.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 x (sqrt.f64 x)) (.f64 x (.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (neg.f64 x) (.f64 x (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x (*.f64 x x)))))
(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (.f64 (neg.f64 x) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
(log.f64 #s(literal 2 binary64))

eval22.0ms (0.6%)

Memory: 2.4MiB live, 39.2MiB allocated
Compiler: Compiled 4 498 to 577 computations (87.2% saved)

prune26.0ms (0.8%)

Memory

8.6MiB live, 51.9MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	203	9	212

Accuracy

100.0%

Counts

212 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	10.0%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
▶	20.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
▶	19.6%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
✓	55.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	50.6%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	50.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	50.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.7%	#s(literal 0 binary64)

Compiler

Compiled 87 to 49 computations (43.7% saved)

simplify720.0ms (20.9%)

Memory

22.6MiB live, 891.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
cost-diff	1600	(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
cost-diff	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
cost-diff	0	(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))
cost-diff	0	(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
cost-diff	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
cost-diff	0	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
cost-diff	12288	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Rules

30 288×	`lower-fma.f64`
30 288×	`lower-fma.f32`
4 114×	`lower-*.f32`
4 092×	`lower-*.f64`
2 320×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	285
0	59	251
1	112	225
2	286	188
3	648	174
4	1078	174
5	1445	172
6	1656	172
7	1884	172
8	2085	172
9	2832	172
10	4650	172
11	5646	172
12	6243	172
13	6512	172
14	6539	172
15	6956	172
16	7717	172
17	7757	172
18	7757	172
19	7757	172
20	7881	172
0	8869	169

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
x
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
#s(literal 2 binary64)
#s(literal 1/4 binary64)
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
x
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(neg.f64 (*.f64 x x))
(*.f64 x x)
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 x (.f64 x x))
x
(*.f64 x x)
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x))))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))
(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (.f64 x x) (*.f64 x (sqrt.f64 x)))
(*.f64 x x)
x
(*.f64 x (sqrt.f64 x))
(sqrt.f64 x)
(*.f64 x (+.f64 x x))
(+.f64 x x)

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

localize120.0ms (3.5%)

Memory

13.6MiB live, 237.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0625	(.f64 (.f64 x x) (*.f64 x (sqrt.f64 x)))
accuracy	0.0703125	(*.f64 x (sqrt.f64 x))
accuracy	6.13704077893481	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x))))
accuracy	18.592530036812374	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
accuracy	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
accuracy	0.0390625	(.f64 x (.f64 x x))
accuracy	0.1171875	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
accuracy	18.592530036812374	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
accuracy	0.05078125	(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
accuracy	0.11947250976844201	(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))
accuracy	18.592530036812374	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
accuracy	23.043721532688572	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))
accuracy	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
accuracy	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
accuracy	0.2265625	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy	0.5	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Samples

43.0ms	128×	0	valid
39.0ms	128×	0	invalid

Compiler

Compiled 241 to 33 computations (86.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-mult: 34.0ms (50.8% of total)

ival-pow2: 14.0ms (20.9% of total)

ival-sqrt: 8.0ms (11.9% of total)

ival-pow: 4.0ms (6% of total)

ival-div: 3.0ms (4.5% of total)

ival-add: 3.0ms (4.5% of total)

ival-neg: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.3%)

Memory

-13.7MiB live, 25.4MiB allocated

Counts

19 → 192

Calls

Call 1

Inputs
#<alt (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))>
#<alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))>
#<alt (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))>
#<alt (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))>
#<alt (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))>
#<alt #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))>
#<alt (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))>
#<alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))>
#<alt (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))>
#<alt #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))>
#<alt (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))>
#<alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))>
#<alt (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x))))>
#<alt (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))>
#<alt (.f64 x (.f64 x x))>
#<alt (*.f64 x (sqrt.f64 x))>
#<alt (.f64 (.f64 x x) (*.f64 x (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 (* -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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (sqrt 2)))>
#<alt (* -1 (* (pow x 2) (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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* -1 (* (pow x 4) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (pow x 4) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (pow x 4) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (pow x 4) (pow (sqrt -1) 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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* -2 (* (pow x 6) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (pow x 6) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (pow x 6) (pow (sqrt -1) 2)))>
#<alt (* -2 (* (pow x 6) (pow (sqrt -1) 2)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (sqrt (pow x 7))>
#<alt (* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))>

Calls

48 calls:

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

simplify127.0ms (3.7%)

Memory

13.9MiB live, 133.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 288×	`lower-*.f64`
1 288×	`lower-fma.f64`
1 288×	`lower-fma.f32`
1 288×	`lower-*.f32`
622×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	976
1	91	976
2	269	976
3	554	976
4	902	976
5	1223	976
6	1508	976
7	1965	976
8	2312	976
9	2440	976
10	2500	976
11	2517	976
12	2521	976
13	2521	976
14	2541	976
15	2549	976
16	2549	976
17	2549	976
18	2712	976
0	2712	976

Stop Event

1×	iter limit
1×	saturated

Counts

192 → 192

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 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)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 2) (sqrt 2)))
(* -1 (* (pow x 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))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 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))))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(sqrt (pow x 7))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 2) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x (*.f64 x x))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 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 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (sqrt.f64 #s(literal -2 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (sqrt.f64 #s(literal -2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal -2 binary64)))))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal -2 binary64)))))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal -2 binary64)))))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 x (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x (.f64 x (sqrt.f64 #s(literal -2 binary64)))))))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 x (.f64 x x)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 x (.f64 x x)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 x (.f64 x x)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(sqrt (pow x 7))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))
(* -1 (* (sqrt (pow x 7)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 7 binary64)))

rewrite254.0ms (7.4%)

Memory

-51.3MiB live, 287.0MiB allocated

Rules

3 052×	`lower-fma.f64`
3 052×	`lower-fma.f32`
2 782×	`lower-*.f32`
2 772×	`lower-*.f64`
1 716×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	252
0	59	156
1	188	70
2	1138	49
3	7259	49
0	8411	49

Stop Event

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

Counts

19 → 648

Calls

Call 1

Inputs
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))
(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
(sqrt.f64 #s(literal 2 binary64))
(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x))))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))
(.f64 x (.f64 x x))
(*.f64 x (sqrt.f64 x))
(.f64 (.f64 x x) (*.f64 x (sqrt.f64 x)))

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

eval246.0ms (7.2%)

Memory: 24.6MiB live, 175.3MiB allocated
Compiler: Compiled 20 303 to 2 283 computations (88.8% saved)

prune94.0ms (2.7%)

Memory

13.3MiB live, 174.9MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	857	1	858
Fresh	0	0	0
Picked	1	3	4
Done	0	5	5
Total	858	9	867

Accuracy

100.0%

Counts

867 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	19.8%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 x x) (sqrt.f64 x)) (sqrt.f64 x)))) (*.f64 x x))
✓	20.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
✓	19.6%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
✓	55.5%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	50.6%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	50.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	50.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.7%	#s(literal 0 binary64)

Compiler

Compiled 238 to 94 computations (60.5% saved)

regimes20.0ms (0.6%)

Memory

-4.0MiB live, 35.1MiB allocated

Counts

14 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

6.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
5.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
5.0ms	x
4.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
100.0%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes16.0ms (0.5%)

Memory

-5.2MiB live, 33.1MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (.f64 x x))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 x x) (sqrt.f64 x)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x)) (.f64 x (+.f64 x x)))) (*.f64 x x))

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

Calls

4 calls:

5.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
4.0ms	x
3.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
77.7%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
77.7%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
77.7%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes6.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
50.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
50.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
50.7%	1	`(pow.f64 x #s(literal 2 binary64))`
50.7%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes6.0ms (0.2%)

Memory

-24.6MiB live, 13.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.7%	1	`x`
3.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.7%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch12.0ms (0.3%)

Memory

24.2MiB live, 24.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-8.503899590241208e-306	9.287819662696015e-304

Samples

6.0ms

144×

valid

Compiler

Compiled 147 to 107 computations (27.2% saved)

Precisions

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

ival-pow2: 2.0ms (58% of total)

ival-add: 1.0ms (29% of total)

ival-sqrt: 1.0ms (29% of total)

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

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

simplify20.0ms (0.6%)

Memory

-56.9MiB live, 10.2MiB 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	15	48
1	23	48
2	32	48
3	37	48
4	39	48

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 0 binary64)

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(literal 0 binary64)

soundness79.0ms (2.3%)

Memory

16.3MiB live, 92.6MiB allocated

Rules

180×	`lower-*.f32`
176×	`lower-*.f64`
142×	`lower-fma.f32`
140×	`lower-fma.f64`
104×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	21	112
0	36	57
1	116	36
0	896	36
0	5	18
0	8	14
1	28	10
0	170	9

Stop Event

1×	fuel
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated

Compiler

Compiled 70 to 38 computations (45.7% saved)

preprocess35.0ms (1%)

Memory: -0.8MiB live, 77.5MiB allocated
Compiler: Compiled 68 to 30 computations (55.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	15	612
1	30	612
2	65	612
3	113	612
4	132	612
5	173	612
6	207	612
7	236	612
8	273	612
9	278	612
0	278	612

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	21	112
0	36	57
1	116	36
0	896	36
0	5	18
0	8	14
1	28	10
0	170	9

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	15	612
1	30	612
2	65	612
3	113	612
4	132	612
5	173	612
6	207	612
7	236	612
8	273	612
9	278	612
0	278	612

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	21	112
0	36	57
1	116	36
0	896	36
0	5	18
0	8	14
1	28	10
0	170	9

start0.0ms (0%)

analyze0.0ms (0%)

sample566.0ms (16.5%)

explain69.0ms (2%)

preprocess18.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.2%)

localize18.0ms (0.5%)

series3.0ms (0.1%)

simplify9.0ms (0.3%)

rewrite38.0ms (1.1%)

eval8.0ms (0.2%)

prune8.0ms (0.2%)

simplify262.0ms (7.6%)

localize82.0ms (2.4%)

series4.0ms (0.1%)

simplify15.0ms (0.4%)

rewrite122.0ms (3.6%)

eval28.0ms (0.8%)

prune19.0ms (0.6%)

simplify12.0ms (0.3%)

localize117.0ms (3.4%)

series2.0ms (0.1%)

simplify16.0ms (0.5%)

rewrite199.0ms (5.8%)

eval22.0ms (0.6%)

prune26.0ms (0.8%)

simplify720.0ms (20.9%)

localize120.0ms (3.5%)

series11.0ms (0.3%)

simplify127.0ms (3.7%)

rewrite254.0ms (7.4%)

eval246.0ms (7.2%)

prune94.0ms (2.7%)

regimes20.0ms (0.6%)

regimes16.0ms (0.5%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

bsearch12.0ms (0.3%)

simplify20.0ms (0.6%)

soundness79.0ms (2.3%)

preprocess35.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	15	612
1	30	612
2	65	612
3	113	612
4	132	612
5	173	612
6	207	612
7	236	612
8	273	612
9	278	612
0	278	612

Iter	Nodes	Cost
0	15	324
1	29	324
2	60	324
3	107	324
4	126	324
5	167	324
6	201	324
7	230	324
8	260	324
9	262	324
0	262	324

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	21	112
0	36	57
1	116	36
0	896	36
0	5	18
0	8	14
1	28	10
0	170	9