Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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 4 computations (60% saved)

sample605.0ms (17.4%)

Memory

-9.8MiB live, 977.6MiB allocated

Samples

431.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 223.0ms

ival-hypot: 213.0ms (95.7% of total)

ival-true: 6.0ms (2.7% of total)

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

Bogosity

preprocess29.0ms (0.8%)

Memory

-19.8MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Rules

42×	`associate-r`
32×	`distribute-lft-neg-in`
32×	`sub-neg`
24×	`neg-sub0`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

explain107.0ms (3.1%)

Memory

10.5MiB live, 89.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	2	(1.4097574924722788e-158)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	65	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	65
↳	`(*.f64 x x)`	underflow	130
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	55	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	55
↳	`(*.f64 x x)`	overflow	110

Confusion

	Predicted +	Predicted -
+	120	2
-	0	134

Precision

1.0

Recall

0.9836065573770492

Confusion?

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

Precision?

1.0

Recall?

0.9836065573770492

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 60 to 20 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 23.0ms (68.3% of total)

ival-hypot: 8.0ms (23.8% of total)

ival-add: 2.0ms (5.9% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	cost-diff	320	(+.f64 (.f64 x x) (.f64 x x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
1	11	15
2	14	15
3	17	15
0	17	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (1%)

Memory

-14.5MiB live, 24.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 x x))
✓	accuracy	56.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

28.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-hypot: 20.0ms (87.1% of total)

ival-mult: 2.0ms (8.7% of total)

ival-add: 1.0ms (4.4% of total)

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

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

series4.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<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)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

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

rewrite40.0ms (1.1%)

Memory

10.4MiB live, 51.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

66×	`lower-*.f32`
64×	`lower-*.f64`
42×	`lower-fma.f64`
42×	`lower-fma.f32`
34×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

simplify11.0ms (0.3%)

Memory

-24.3MiB live, 15.2MiB 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
(* 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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

eval600.0ms (17.3%)

Memory: -7.4MiB live, 31.6MiB allocated
Compiler: Compiled 702 to 94 computations (86.6% saved)

prune7.0ms (0.2%)

Memory

27.4MiB live, 27.4MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Accuracy

100.0%

Counts

86 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	19.2%	(/.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))))
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Compiler

Compiled 100 to 50 computations (50% saved)

simplify19.0ms (0.6%)

Memory

-14.5MiB live, 24.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	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	(sqrt.f64 (+.f64 x x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(*.f64 (+.f64 x x) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	5312	(hypot.f64 x x)

Rules

352×	`lower-*.f32`
340×	`lower-*.f64`
308×	`lower-fma.f32`
306×	`lower-fma.f64`
298×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	128
0	37	114
1	52	102
2	104	87
3	192	81
4	255	81
5	505	81
6	540	81
7	541	81
0	541	81

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize90.0ms (2.6%)

Memory

5.3MiB live, 89.2MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	84.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	accuracy	77.0%	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
✓	accuracy	37.9%	(/.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	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 (+.f64 x x) x)
✓	accuracy	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(hypot.f64 x x)

Samples

70.0ms

256×

valid

Compiler

Compiled 141 to 22 computations (84.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-hypot: 27.0ms (46.1% of total)

ival-mult: 11.0ms (18.8% of total)

ival-add: 10.0ms (17.1% of total)

ival-sqrt: 9.0ms (15.4% of total)

ival-div: 1.0ms (1.7% of total)

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

exact: 0.0ms (0% of total)

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

series51.0ms (1.5%)

Memory

-16.7MiB live, 20.4MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>
#<alt (*.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (*.f64 (+.f64 x x) x))>
#<alt (*.f64 (+.f64 x x) x)>
#<alt (+.f64 x x)>
#<alt (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))>
#<alt (sqrt.f64 x)>
#<alt (sqrt.f64 (+.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 (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (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 (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (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
38.0ms	x	@	0	(/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (sqrt (+ (* (* x x) (* x x)) 0)))
1.0ms	x	@	-inf	(* (sqrt x) (sqrt (+ x x)))
1.0ms	x	@	-inf	(sqrt (+ x x))
0.0ms	x	@	inf	(sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x))))
0.0ms	x	@	-inf	(sqrt x)

rewrite51.0ms (1.5%)

Memory

9.6MiB live, 46.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	93
0	37	43
1	105	23
0	823	23

Stop Event

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

Counts

13 → 59

Calls

Call 1

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

simplify303.0ms (8.7%)

Memory

14.2MiB live, 175.0MiB allocated

Algorithm

1×	egg-herbie

Rules

1 808×	`lower-*.f64`
1 808×	`lower-fma.f64`
1 808×	`lower-fma.f32`
1 808×	`lower-*.f32`
1 768×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	612
1	63	612
2	168	612
3	337	612
4	579	612
5	920	612
6	1535	612
7	1673	612
8	1758	612
9	1845	612
10	1911	612
11	1956	612
12	1972	612
13	1976	612
14	1976	612
15	2080	612
16	2339	612
17	2781	612
18	3397	612
19	3463	612
20	3577	612
21	3635	612
22	3695	612
23	4027	612
24	4163	612
25	4163	612
26	4163	612
27	4163	612
28	4639	612
29	4811	612
30	4847	612
31	4861	612
32	4863	612
33	4863	612
34	5067	612
0	5067	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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (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)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(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)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 x (.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal -1 binary64)))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (sqrt.f64 #s(literal -2 binary64)) (neg.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 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 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))

eval31.0ms (0.9%)

Memory: -26.1MiB live, 53.5MiB allocated
Compiler: Compiled 4 410 to 286 computations (93.5% saved)

prune13.0ms (0.4%)

Memory

36.4MiB live, 36.4MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	265	8	273

Accuracy

100.0%

Counts

273 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.3%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
▶	99.0%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	99.1%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 63 to 39 computations (38.1% saved)

simplify27.0ms (0.8%)

Memory

-31.4MiB live, 46.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	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	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1600	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	cost-diff	0	(log.f64 #s(literal 2 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	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

460×	`lower-*.f32`
446×	`lower-*.f64`
422×	`associate-r`
422×	`lower-fma.f32`
420×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	110
0	35	100
1	57	88
2	119	74
3	215	68
4	295	68
5	678	68
6	732	68
7	737	68
8	743	68
9	747	68
10	748	68
0	748	68

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (2.2%)

Memory

20.6MiB live, 102.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	84.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	accuracy	37.9%	(/.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	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	98.4%	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

52.0ms

256×

valid

Compiler

Compiled 116 to 22 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 26.0ms (63.4% of total)

ival-sqrt: 5.0ms (12.2% of total)

ival-log: 3.0ms (7.3% of total)

ival-div: 2.0ms (4.9% of total)

ival-add: 2.0ms (4.9% of total)

ival-exp: 2.0ms (4.9% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.3%)

Memory

-12.9MiB live, 25.6MiB allocated

Counts

12 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite172.0ms (5%)

Memory

8.2MiB live, 330.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 630×	`lower-fma.f32`
3 628×	`lower-fma.f64`
1 716×	`lower-+.f64`
1 716×	`lower-+.f32`
1 644×	`lower-exp.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	91
0	35	41
1	100	39
2	626	21
3	4541	21
0	8774	21

Stop Event

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

Counts

12 → 205

Calls

Call 1

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

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

simplify123.0ms (3.5%)

Memory

11.3MiB live, 90.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 140×	`lower-*.f64`
1 140×	`lower-*.f32`
1 136×	`lower-fma.f64`
1 136×	`lower-fma.f32`
654×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	404
1	59	404
2	176	404
3	362	404
4	1063	404
5	1734	404
6	2115	404
7	2211	404
8	2243	404
9	2251	404
10	2251	404
11	2431	404
12	2503	404
13	2503	404
14	2503	404
15	2503	404
16	2565	404
0	2565	404

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

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

eval36.0ms (1%)

Memory: -3.9MiB live, 70.7MiB allocated
Compiler: Compiled 6 141 to 878 computations (85.7% saved)

prune33.0ms (0.9%)

Memory

5.8MiB live, 87.8MiB allocated

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	0	0	0
Picked	2	2	4
Done	0	4	4
Total	332	11	343

Accuracy

100.0%

Counts

343 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	35.7%	(/.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
▶	15.1%	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x)))) (*.f64 x x))
▶	99.2%	(.f64 (/.f64 x (sqrt.f64 x)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
▶	99.2%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 x))))
✓	99.0%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.1%	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 191 to 105 computations (45% saved)

simplify387.0ms (11.2%)

Memory

-5.1MiB live, 428.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	cost-diff	0	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	cost-diff	12288	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x)))
✓	cost-diff	0	(sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x))))
✓	cost-diff	0	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	cost-diff	2944	(/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 x (sqrt.f64 x))
✓	cost-diff	2304	(.f64 (/.f64 x (sqrt.f64 x)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	1664	(/.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	2304	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 x))))

Rules

9 756×	`lower-*.f32`
9 726×	`lower-*.f64`
7 606×	`lower-fma.f64`
7 606×	`lower-fma.f32`
2 530×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	286
0	55	262
1	108	218
2	319	170
3	1496	130
4	2048	130
5	3139	130
6	5365	130
7	6850	130
8	7420	130
9	7566	130
10	7678	130
11	7772	130
0	9750	130

Stop Event

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

Calls

Call 1

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

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

localize96.0ms (2.8%)

Memory

-8.4MiB live, 148.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
✓	accuracy	99.3%	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	accuracy	98.4%	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	84.8%	(sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x))))
✓	accuracy	37.9%	(/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	accuracy	23.1%	(/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x x))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(.f64 (/.f64 x (sqrt.f64 x)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x)))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))
✓	accuracy	99.8%	(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.8%	(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	37.9%	(/.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 x))))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 x)))
✓	accuracy	99.2%	(/.f64 x (sqrt.f64 x))

Samples

59.0ms

256×

valid

Compiler

Compiled 288 to 31 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 22.0ms (50% of total)

ival-pow: 7.0ms (15.9% of total)

ival-div: 6.0ms (13.6% of total)

ival-sqrt: 5.0ms (11.4% of total)

ival-pow2: 2.0ms (4.5% of total)

ival-add: 1.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.7%)

Memory

2.9MiB live, 43.3MiB allocated

Counts

19 → 192

Calls

Call 1

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

48 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* (/ (* x (* x (* (* x x) (* x (* x (* x x)))))) (* x (* x (* x x)))) (* x (+ x x)))
2.0ms	x	@	-inf	(/ x (sqrt x))
1.0ms	x	@	-inf	(* (sqrt 2) (/ x (sqrt x)))
1.0ms	x	@	-inf	(* x (* x (* x (sqrt 2))))
1.0ms	x	@	-inf	(* (/ (* x (* x (* (* x x) (* x (* x (* x x)))))) (* x (* x (* x x)))) (* x (+ x x)))

rewrite62.0ms (1.8%)

Memory

12.3MiB live, 88.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

686×	`lower-*.f32`
656×	`lower-*.f64`
496×	`lower-/.f32`
488×	`lower-/.f64`
94×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	206
0	55	171
1	164	129
0	936	126

Stop Event

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

Counts

19 → 282

Calls

Call 1

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

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

simplify136.0ms (3.9%)

Memory

-17.5MiB live, 107.1MiB allocated

Algorithm

1×	egg-herbie

Rules

1 236×	`associate-r`
1 140×	`lower-*.f64`
1 140×	`lower-*.f32`
1 136×	`lower-fma.f64`
1 136×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	812
1	54	812
2	145	812
3	287	812
4	606	812
5	860	812
6	1283	812
7	1749	812
8	1899	812
9	1925	812
10	1925	812
11	1925	812
12	2234	812
13	2480	812
14	2527	812
15	2545	812
16	2547	812
17	2547	812
18	2851	812
0	2851	812

Stop Event

1×	iter limit
1×	saturated

Counts

192 → 192

Calls

Call 1

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

eval55.0ms (1.6%)

Memory: 37.6MiB live, 111.0MiB allocated
Compiler: Compiled 9 362 to 917 computations (90.2% saved)

prune46.0ms (1.3%)

Memory

-24.1MiB live, 92.0MiB allocated

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	580	7	587
Fresh	0	0	0
Picked	4	1	5
Done	1	5	6
Total	585	13	598

Accuracy

100.0%

Counts

598 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	35.7%	(/.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
	99.3%	(/.f64 (sqrt.f64 (+.f64 x x)) (/.f64 (sqrt.f64 x) x))
	99.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
	99.4%	(*.f64 (/.f64 x (sqrt.f64 x)) (sqrt.f64 (+.f64 x x)))
	71.1%	(.f64 (.f64 x (sqrt.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	99.2%	(.f64 (sqrt.f64 x) (.f64 x (/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 x))))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	99.2%	(*.f64 x (/.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
	99.1%	(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (+.f64 x x))))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 350 to 142 computations (59.4% saved)

regimes26.0ms (0.8%)

Memory

7.5MiB live, 45.2MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

8.0ms	x
6.0ms	(*.f64 x x)
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
6.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes26.0ms (0.8%)

Memory

-1.8MiB live, 39.6MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
6.0ms	x
5.0ms	(*.f64 x x)
5.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes8.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB 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	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(*.f64 x x)
1.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
3.9%	1	`x`
3.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.9%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.9%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify7.0ms (0.2%)

Memory

-20.8MiB live, 17.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	12	15

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(hypot.f64 x x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 0 binary64)

soundness90.0ms (2.6%)

Memory

9.5MiB live, 119.4MiB allocated

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	93
0	37	43
1	105	23
0	823	23
0	4	18
0	7	14
1	23	10
0	160	9
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×	fuel
1×	iter limit
1×	saturated
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

Compiler

Compiled 39 to 25 computations (35.9% saved)

preprocess27.0ms (0.8%)

Memory: 25.7MiB live, 64.9MiB allocated
Remove: (abs x)
Compiler: Compiled 58 to 32 computations (44.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	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	19	128
0	37	114
1	52	102
2	104	87
3	192	81
4	255	81
5	505	81
6	540	81
7	541	81
0	541	81

Iter	Nodes	Cost
0	19	110
0	35	100
1	57	88
2	119	74
3	215	68
4	295	68
5	678	68
6	732	68
7	737	68
8	743	68
9	747	68
10	748	68
0	748	68

Iter	Nodes	Cost
0	19	93
0	37	43
1	105	23
0	823	23
0	4	18
0	7	14
1	23	10
0	160	9
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	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	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	19	128
0	37	114
1	52	102
2	104	87
3	192	81
4	255	81
5	505	81
6	540	81
7	541	81
0	541	81

Iter	Nodes	Cost
0	19	110
0	35	100
1	57	88
2	119	74
3	215	68
4	295	68
5	678	68
6	732	68
7	737	68
8	743	68
9	747	68
10	748	68
0	748	68

Iter	Nodes	Cost
0	19	93
0	37	43
1	105	23
0	823	23
0	4	18
0	7	14
1	23	10
0	160	9
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

analyze0.0ms (0%)

sample605.0ms (17.4%)

preprocess29.0ms (0.8%)

explain107.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize33.0ms (1%)

series4.0ms (0.1%)

rewrite40.0ms (1.1%)

simplify11.0ms (0.3%)

eval600.0ms (17.3%)

prune7.0ms (0.2%)

simplify19.0ms (0.6%)

localize90.0ms (2.6%)

series51.0ms (1.5%)

rewrite51.0ms (1.5%)

simplify303.0ms (8.7%)

eval31.0ms (0.9%)

prune13.0ms (0.4%)

simplify27.0ms (0.8%)

localize76.0ms (2.2%)

series12.0ms (0.3%)

rewrite172.0ms (5%)

simplify123.0ms (3.5%)

eval36.0ms (1%)

prune33.0ms (0.9%)

simplify387.0ms (11.2%)

localize96.0ms (2.8%)

series23.0ms (0.7%)

rewrite62.0ms (1.8%)

simplify136.0ms (3.9%)

eval55.0ms (1.6%)

prune46.0ms (1.3%)

regimes26.0ms (0.8%)

regimes26.0ms (0.8%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

simplify7.0ms (0.2%)

soundness90.0ms (2.6%)

preprocess27.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	8
0	7	6
1	11	6
2	14	6
3	17	6
0	17	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	19	128
0	37	114
1	52	102
2	104	87
3	192	81
4	255	81
5	505	81
6	540	81
7	541	81
0	541	81

Iter	Nodes	Cost
0	19	110
0	35	100
1	57	88
2	119	74
3	215	68
4	295	68
5	678	68
6	732	68
7	737	68
8	743	68
9	747	68
10	748	68
0	748	68

Iter	Nodes	Cost
0	19	93
0	37	43
1	105	23
0	823	23
0	4	18
0	7	14
1	23	10
0	160	9
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