Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample561.0ms (26.1%)

Memory

2.8MiB live, 742.1MiB allocated

Samples

364.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 227.0ms

ival-pow2: 124.0ms (54.6% of total)

ival-sqrt: 58.0ms (25.6% of total)

ival-add: 37.0ms (16.3% of total)

ival-true: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain67.0ms (3.1%)

Memory

26.8MiB live, 104.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
119	-	2	(-1.9459335138386085e-159)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	59	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	59
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	118
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	58	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	58
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	116

Confusion

	Predicted +	Predicted -
+	117	2
-	0	137

Precision

1.0

Recall

0.9831932773109243

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	2
-	0	0	137

Precision?

1.0

Recall?

0.9831932773109243

Freqs

test

number	freq
0	139
1	117

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

512×

valid

Compiler

Compiled 53 to 19 computations (64.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 6.0ms (48.3% of total)

ival-sqrt: 4.0ms (32.2% of total)

ival-add: 2.0ms (16.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess21.0ms (1%)

Memory

-24.5MiB live, 19.7MiB 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: 0.4MiB live, 0.4MiB 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
▶	57.3%	(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)

simplify4.0ms (0.2%)

Memory

5.0MiB live, 5.0MiB 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)

localize21.0ms (1%)

Memory

-12.5MiB live, 25.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
accuracy	27.318734222241872	(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 (50.3% of total)

ival-sqrt: 2.0ms (33.5% of total)

ival-add: 1.0ms (16.8% 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

3.7MiB live, 3.7MiB 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))

simplify6.0ms (0.3%)

Memory

7.5MiB live, 7.5MiB 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 (1.7%)

Memory

0.2MiB live, 37.7MiB 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 (0.4%)

Memory: 15.1MiB live, 15.1MiB allocated
Compiler: Compiled 774 to 104 computations (86.6% saved)

prune10.0ms (0.5%)

Memory

-21.7MiB live, 16.8MiB 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)
▶	19.4%	(/.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))))
▶	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	52.2%	#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)

simplify241.0ms (11.2%)

Memory

25.8MiB live, 104.4MiB 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 (3.8%)

Memory

-9.6MiB live, 108.6MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	16.279645341450717	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.17185978894967	(/.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	27.318734222241872	(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	0.3984375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	30.41371830025671	#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	0.3984375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	32.14178517127712	#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

44.0ms

256×

valid

Compiler

Compiled 153 to 22 computations (85.6% saved)

Precisions

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

ival-sqrt: 10.0ms (31% of total)

ival-mult: 9.0ms (27.9% of total)

ival-hypot: 5.0ms (15.5% of total)

ival-add: 3.0ms (9.3% of total)

ival-div: 2.0ms (6.2% of total)

ival-pow2: 2.0ms (6.2% of total)

ival-neg: 1.0ms (3.1% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB 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)
0.0ms	x	@	inf	(* x (+ x x))
0.0ms	x	@	0	(+ x x)
0.0ms	x	@	0	(+ (* (* x x) (* x x)) 0)

simplify18.0ms (0.8%)

Memory

-13.5MiB live, 23.2MiB 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)))

rewrite51.0ms (2.4%)

Memory

24.5MiB live, 60.7MiB 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)

eval85.0ms (3.9%)

Memory: -39.9MiB live, 57.0MiB allocated
Compiler: Compiled 5 055 to 302 computations (94% saved)

prune21.0ms (1%)

Memory

3.9MiB live, 44.6MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	293	5	298
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	294	9	303

Accuracy

100.0%

Counts

303 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.6%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
▶	19.4%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
▶	12.9%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
✓	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	49.3%	#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)))))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 176 to 95 computations (46% saved)

simplify19.0ms (0.9%)

Memory

-9.7MiB live, 29.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.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	#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)))) (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 (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

400×	`lower-*.f32`
384×	`lower-*.f64`
334×	`associate-r`
308×	`lower-fma.f32`
306×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	296
0	57	226
1	87	196
2	159	179
3	252	163
4	342	163
5	616	163
6	651	163
7	652	163
0	652	160

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize134.0ms (6.2%)

Memory

24.8MiB live, 142.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
accuracy	16.279645341450703	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.17185978894967	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
accuracy	0.171875	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
accuracy	16.279645341450703	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	24.62115009872443	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
accuracy	40.17185978894967	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
accuracy	0.049160009768442016	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	40.17185978894967	(/.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	0.3984375	(.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	32.14178517127712	#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

55.0ms

256×

valid

Compiler

Compiled 284 to 30 computations (89.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 14.0ms (36% of total)

ival-sqrt: 8.0ms (20.5% of total)

ival-div: 4.0ms (10.3% of total)

ival-add: 3.0ms (7.7% of total)

ival-exp: 3.0ms (7.7% of total)

ival-log: 3.0ms (7.7% of total)

ival-pow2: 3.0ms (7.7% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

15 → 144

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

Calls

36 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	@	-inf	(* (sqrt 2) (* x (* x x)))
0.0ms	x	@	inf	(/ (sqrt (* (* (* x (* x x)) x) (* x (+ x x)))) (sqrt (+ (* (* x x) (* x x)) 0)))
0.0ms	x	@	-inf	(/ (sqrt (* (* (* x (* x x)) x) (* x (+ x x)))) (sqrt (+ (* (* x x) (* x x)) 0)))

simplify16.0ms (0.8%)

Memory

-18.6MiB live, 20.4MiB 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	16	688
1	30	688
2	63	688
3	113	688
4	132	688
5	173	688
6	207	688
7	236	688
8	266	688
9	268	688
0	268	688

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

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

rewrite80.0ms (3.7%)

Memory

15.4MiB live, 54.0MiB allocated

Rules

202×	`lower-*.f32`
190×	`lower-*.f64`
150×	`lower-/.f32`
148×	`lower-/.f64`
140×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	203
0	57	115
1	160	55
0	988	55

Stop Event

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

Counts

15 → 85

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

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

eval61.0ms (2.8%)

Memory: 6.0MiB live, 48.5MiB allocated
Compiler: Compiled 6 271 to 364 computations (94.2% saved)

prune23.0ms (1.1%)

Memory

10.7MiB live, 48.1MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	336	2	338
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	339	8	347

Accuracy

100.0%

Counts

347 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.6%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
▶	16.6%	(/.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))
✓	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.3%	#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)))))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 68 to 40 computations (41.2% saved)

simplify21.0ms (1%)

Memory

-27.5MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(.f64 (.f64 x (*.f64 x x)) x)
cost-diff	0	(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x 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))

Rules

138×	`lower-*.f32`
126×	`lower-*.f64`
114×	`lower-fma.f64`
114×	`lower-fma.f32`
92×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	143
0	33	117
1	59	105
2	116	95
3	205	85
4	238	85
0	238	85

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.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 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 x (.f64 x x))
x
(*.f64 x x)
(*.f64 x (+.f64 x x))
(+.f64 x x)

Outputs
(/.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 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
(/.f64 (sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (+.f64 x x)))) (.f64 x x))
(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 x (+.f64 x x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
(.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 x (+.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 x (.f64 x (*.f64 x x)))
(.f64 x (.f64 x x))
x
(*.f64 x x)
(*.f64 x (+.f64 x x))
(+.f64 x x)

localize58.0ms (2.7%)

Memory

13.5MiB live, 93.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(.f64 (.f64 x (*.f64 x x)) x)
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
accuracy	40.17185978894967	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.171875	(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))
accuracy	24.62115009872443	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x))))
accuracy	40.17185978894967	(/.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))

Samples

39.0ms

256×

valid

Compiler

Compiled 127 to 20 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 18.0ms (61.2% of total)

ival-sqrt: 5.0ms (17% of total)

ival-div: 3.0ms (10.2% of total)

ival-add: 2.0ms (6.8% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#<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 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))>
#<alt (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))>
#<alt (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))>
#<alt (.f64 (.f64 x (*.f64 x x)) x)>
#<alt (.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 (* (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 (* 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))>
#<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 (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)>

Calls

24 calls:

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

simplify17.0ms (0.8%)

Memory

-12.7MiB live, 22.6MiB 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	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

Calls

Call 1

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

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

rewrite170.0ms (7.9%)

Memory

5.3MiB live, 175.2MiB allocated

Rules

3 826×	`lower-fma.f64`
3 826×	`lower-fma.f32`
1 710×	`lower-+.f64`
1 710×	`lower-+.f32`
1 630×	`prod-exp`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	121
0	33	100
1	102	32
2	623	32
3	4365	22
0	8638	22

Stop Event

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

Counts

9 → 251

Calls

Call 1

Inputs
(/.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 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 x (.f64 x x))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)))
(neg.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x))
(/.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(/.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x) x)
(/.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x) (neg.f64 x))
(/.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(/.f64 (neg.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x)) x)
(/.f64 (neg.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(/.f64 (.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))) (*.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x))) (neg.f64 x))
(/.f64 (.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (/.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) #s(literal -1 binary64)) (*.f64 x x))
(pow.f64 (/.f64 (.f64 x x) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 (.f64 x x) #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) (/.f64 (.f64 x x) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))) #s(literal -1/2 binary64))
(.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))))
(.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal -1 binary64) (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)))
(.f64 (neg.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x)) (/.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x))
(.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x))
(.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) x)))
(.f64 (pow.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x))
(.f64 (/.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
(.f64 (/.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x))
(.f64 (/.f64 (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
(neg.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))
(.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))))
#s(literal 0 binary64)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 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 (log.f64 (exp.f64 (log.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 (exp.f64 (log.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 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.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(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(exp.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #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)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (log.f64 x))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64) (log.f64 (.f64 x x))))
(exp.f64 (fma.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64) (log.f64 (.f64 x x))))
(exp.f64 (fma.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64) (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64) (.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64))))
(exp.f64 (fma.f64 #s(literal 3 binary64) (log.f64 x) (*.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64) (.f64 #s(literal -4 binary64) (log.f64 x))))
(exp.f64 (fma.f64 (log.f64 (.f64 x x)) #s(literal 4 binary64) (.f64 #s(literal -4 binary64) (log.f64 x))))
(exp.f64 (fma.f64 (.f64 #s(literal 5 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 5 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 #s(literal -4 binary64) (log.f64 x) (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 #s(literal -4 binary64) (log.f64 x) (.f64 (log.f64 (.f64 x x)) #s(literal 4 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (.f64 (.f64 #s(literal 5 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 5 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(fabs.f64 (.f64 x (.f64 x (*.f64 x x))))
(-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(sqrt.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 x (neg.f64 (.f64 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 x 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 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.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 x x)))) (/.f64 #s(literal 1 binary64) (.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 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.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 x (.f64 x (.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 (.f64 x (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x 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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.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 x)))) (.f64 (.f64 x (.f64 x (.f64 x 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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.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 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (/.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.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 x (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.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 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (.f64 x 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 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x 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 (.f64 x x)))))) (.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 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 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 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.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 (.f64 x x))))) (.f64 x x))
(/.f64 (pow.f64 x #s(literal 36 binary64)) (pow.f64 (*.f64 x x) #s(literal 16 binary64)))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))))
(/.f64 (pow.f64 x #s(literal 24 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.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 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 0 binary64))) #s(literal 1 binary64))
(/.f64 (pow.f64 (*.f64 x x) #s(literal 14 binary64)) (pow.f64 x #s(literal 24 binary64)))
(/.f64 (.f64 (pow.f64 x #s(literal 36 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 x x) #s(literal 16 binary64)))
(/.f64 (.f64 (pow.f64 x #s(literal 24 binary64)) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))))
(/.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x 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 x x)))) (.f64 (.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 x x)))) (.f64 (.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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 4 binary64))
(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 (log.f64 x)) x) #s(literal 2 binary64))
(pow.f64 (*.f64 x (exp.f64 (log.f64 x))) #s(literal 2 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 x (neg.f64 (.f64 x (*.f64 x x))))
(.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))
(.f64 (.f64 x 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 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 (.f64 x (.f64 x (.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 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 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) x))
(.f64 #s(literal -1 binary64) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (*.f64 x 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 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (sqrt.f64 x)) (.f64 x (.f64 x (sqrt.f64 x))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (sqrt.f64 x) (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.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 x (.f64 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.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 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))))
(.f64 (neg.f64 (.f64 x (*.f64 x x))) x)
(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (fma.f64 #s(literal 4 binary64) (log.f64 x) (.f64 #s(literal 3 binary64) (log.f64 x))) (.f64 #s(literal -4 binary64) (log.f64 x))))
(exp.f64 (+.f64 (fma.f64 #s(literal 3 binary64) (log.f64 x) (.f64 #s(literal 4 binary64) (log.f64 x))) (.f64 #s(literal -4 binary64) (log.f64 x))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (log.f64 (*.f64 x x))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64))))
(exp.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) (*.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 (.f64 x x)) #s(literal 1 binary64) (.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (*.f64 (log.f64 x) #s(literal 3/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (log.f64 x) #s(literal 3/2 binary64))))
(exp.f64 (fma.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64) (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 x (*.f64 x x))) x)
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.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 x x))
(/.f64 (.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (*.f64 x x)))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 3/8 binary64))
(pow.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -3/4 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) (exp.f64 (log.f64 x)))
(.f64 (.f64 x (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))

eval47.0ms (2.2%)

Memory: 6.9MiB live, 79.0MiB allocated
Compiler: Compiled 8 290 to 1 151 computations (86.1% saved)

prune47.0ms (2.2%)

Memory

-18.9MiB live, 100.0MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	402	2	404
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	402	10	412

Accuracy

100.0%

Counts

412 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	20.6%	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	20.6%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
	16.1%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (sqrt.f64 x)) (.f64 x (sqrt.f64 x))))) (*.f64 x x))
✓	16.6%	(/.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))
✓	57.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.3%	#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)))))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 312 to 107 computations (65.7% saved)

regimes25.0ms (1.2%)

Memory

16.1MiB live, 51.5MiB allocated

Counts

15 → 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 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.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 x (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (sqrt.f64 x)) (.f64 x (sqrt.f64 x))))) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (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))))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x (+.f64 x x)))) (*.f64 x x))
(hypot.f64 x x)
#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:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
5.0ms	x
5.0ms	(pow.f64 x #s(literal 2 binary64))
5.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (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)

regimes20.0ms (0.9%)

Memory

-13.4MiB live, 37.4MiB allocated

Counts

12 → 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 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.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 x (.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 x (sqrt.f64 x)) (.f64 x (sqrt.f64 x))))) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (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))))
(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x 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:

7.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	x
4.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
4.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
80.4%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
80.4%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
80.4%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes7.0ms (0.3%)

Memory

20.6MiB live, 20.6MiB 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:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
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
49.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
49.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
49.4%	1	`(pow.f64 x #s(literal 2 binary64))`
49.4%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes7.0ms (0.3%)

Memory

-19.4MiB live, 18.9MiB 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:

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

Results

Accuracy	Segments	Branch
3.8%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.8%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.8%	1	`(pow.f64 x #s(literal 2 binary64))`
3.8%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch9.0ms (0.4%)

Memory

21.3MiB live, 21.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	-4.556733986893179e-308	7.76888417369085e-308

Samples

5.0ms

112×

valid

Compiler

Compiled 117 to 85 computations (27.4% saved)

Precisions

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

ival-add: 1.0ms (38.8% of total)

ival-sqrt: 1.0ms (38.8% of total)

ival-pow2: 1.0ms (38.8% of total)

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

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

simplify8.0ms (0.4%)

Memory

-21.3MiB live, 16.8MiB 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 -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 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 -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 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)

soundness92.0ms (4.2%)

Memory

8.5MiB live, 155.5MiB 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)

preprocess48.0ms (2.2%)

Memory: 12.0MiB live, 98.3MiB 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	36	296
0	57	226
1	87	196
2	159	179
3	252	163
4	342	163
5	616	163
6	651	163
7	652	163
0	652	160

Iter	Nodes	Cost
0	16	688
1	30	688
2	63	688
3	113	688
4	132	688
5	173	688
6	207	688
7	236	688
8	266	688
9	268	688
0	268	688

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

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	36	296
0	57	226
1	87	196
2	159	179
3	252	163
4	342	163
5	616	163
6	651	163
7	652	163
0	652	160

Iter	Nodes	Cost
0	16	688
1	30	688
2	63	688
3	113	688
4	132	688
5	173	688
6	207	688
7	236	688
8	266	688
9	268	688
0	268	688

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

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%)

sample561.0ms (26.1%)

explain67.0ms (3.1%)

preprocess21.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize21.0ms (1%)

series3.0ms (0.1%)

simplify6.0ms (0.3%)

rewrite38.0ms (1.7%)

eval8.0ms (0.4%)

prune10.0ms (0.5%)

simplify241.0ms (11.2%)

localize82.0ms (3.8%)

series4.0ms (0.2%)

simplify18.0ms (0.8%)

rewrite51.0ms (2.4%)

eval85.0ms (3.9%)

prune21.0ms (1%)

simplify19.0ms (0.9%)

localize134.0ms (6.2%)

series3.0ms (0.1%)

simplify16.0ms (0.8%)

rewrite80.0ms (3.7%)

eval61.0ms (2.8%)

prune23.0ms (1.1%)

simplify21.0ms (1%)

localize58.0ms (2.7%)

series2.0ms (0.1%)

simplify17.0ms (0.8%)

rewrite170.0ms (7.9%)

eval47.0ms (2.2%)

prune47.0ms (2.2%)

regimes25.0ms (1.2%)

regimes20.0ms (0.9%)

regimes7.0ms (0.3%)

regimes7.0ms (0.3%)

bsearch9.0ms (0.4%)

simplify8.0ms (0.4%)

soundness92.0ms (4.2%)

preprocess48.0ms (2.2%)

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	36	296
0	57	226
1	87	196
2	159	179
3	252	163
4	342	163
5	616	163
6	651	163
7	652	163
0	652	160

Iter	Nodes	Cost
0	16	688
1	30	688
2	63	688
3	113	688
4	132	688
5	173	688
6	207	688
7	236	688
8	266	688
9	268	688
0	268	688

Iter	Nodes	Cost
0	15	460
1	29	460
2	60	460
3	107	460
4	125	460
5	166	460
6	200	460
7	229	460
8	259	460
9	261	460
0	261	460

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