Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample938.0ms (32.7%)

Memory

17.5MiB live, 842.1MiB allocated

Samples

771.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 238.0ms

ival-hypot: 229.0ms (96.1% of total)

ival-true: 6.0ms (2.5% of total)

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

Bogosity

explain107.0ms (3.7%)

Memory

-20.5MiB live, 157.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
131	-	-	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	70	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	70
↳	`(*.f64 x x)`	overflow	140
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	61	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	61
↳	`(*.f64 x x)`	underflow	122

Confusion

	Predicted +	Predicted -
+	131	0
-	0	125

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	0	0	125

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

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

ival-hypot: 9.0ms (50.4% of total)

ival-mult: 6.0ms (33.6% of total)

ival-add: 2.0ms (11.2% of total)

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

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

preprocess19.0ms (0.7%)

Memory

0.5MiB live, 36.6MiB 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 (+.f64 x x) x))

Symmetry

(abs x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify3.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
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 (+.f64 x x) x))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (+.f64 x x) x)
(*.f64 x x)
x

localize22.0ms (0.8%)

Memory

-7.5MiB live, 39.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (.f64 x x) (.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	30.514931865002392	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

17.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

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

ival-hypot: 9.0ms (76.9% of total)

ival-mult: 2.0ms (17.1% of total)

ival-add: 1.0ms (8.5% of total)

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

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

series4.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (+.f64 (*.f64 x x) (*.f64 x x)) (patch (+.f64 (*.f64 x x) (*.f64 x x)) #<representation binary64>) () ())

#s(alt (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 x x)) (patch (+.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify8.0ms (0.3%)

Memory

-28.0MiB live, 10.2MiB 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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* -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)

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

rewrite32.0ms (1.1%)

Memory

16.2MiB live, 54.5MiB allocated

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

eval8.0ms (0.3%)

Memory: 20.2MiB live, 20.2MiB allocated
Compiler: Compiled 750 to 96 computations (87.2% saved)

prune12.0ms (0.4%)

Memory

-12.2MiB live, 26.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Accuracy

100.0%

Counts

86 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	14.6%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
	52.0%	(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	52.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 134 to 62 computations (53.7% saved)

simplify18.0ms (0.6%)

Memory

-13.8MiB live, 28.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

352×	`lower-*.f32`
342×	`lower-*.f64`
308×	`lower-fma.f32`
306×	`lower-fma.f64`
294×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	136
0	38	122
1	52	110
2	100	95
3	181	89
4	264	89
5	530	89
6	565	89
7	566	89
0	566	89

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize62.0ms (2.2%)

Memory

-3.3MiB live, 114.0MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.09994125976844202	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.379258878908963	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)))
accuracy	16.332588465273908	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	42.69736909754012	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.33041000976844204	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	30.514931865002392	(sqrt.f64 (*.f64 (+.f64 x x) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.42578125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0.02734375	(hypot.f64 x x)

Samples

39.0ms

256×

valid

Compiler

Compiled 149 to 21 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 9.0ms (33.3% of total)

ival-sqrt: 9.0ms (33.3% of total)

ival-hypot: 5.0ms (18.5% of total)

ival-add: 2.0ms (7.4% of total)

ival-div: 1.0ms (3.7% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.4%)

Memory

21.4MiB live, 21.4MiB allocated

Counts

14 → 156

Calls

Call 1

Inputs
#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (+.f64 x x) x)) (patch (sqrt.f64 (.f64 (+.f64 x x) x)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 x x) x) (patch (.f64 (+.f64 x x) x) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))) (patch (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

((sqrt (+ (* x x) (* x x))) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (sqrt (+ (* (* x x) (* x x)) 0)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))))

2.0ms

inf

((sqrt (+ (* x x) (* x x))) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (sqrt (+ (* (* x x) (* x x)) 0)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))))

2.0ms

((sqrt (+ (* x x) (* x x))) (sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (sqrt (+ (* (* x x) (* x x)) 0)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))))

simplify217.0ms (7.6%)

Memory

6.8MiB live, 48.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 808×	`lower-*.f64`
1 808×	`lower-fma.f64`
1 808×	`lower-fma.f32`
1 808×	`lower-*.f32`
1 664×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	664
1	63	664
2	168	664
3	337	664
4	585	664
5	925	664
6	1461	664
7	1599	664
8	1684	664
9	1771	664
10	1837	664
11	1882	664
12	1896	664
13	1900	664
14	1900	664
15	2000	664
16	2228	664
17	2670	664
18	3286	664
19	3352	664
20	3466	664
21	3524	664
22	3584	664
23	3916	664
24	4052	664
25	4052	664
26	4052	664
27	4052	664
28	4537	664
29	4720	664
30	4756	664
31	4770	664
32	4772	664
33	4772	664
34	4963	664
0	4963	664

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

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

rewrite49.0ms (1.7%)

Memory

-21.4MiB live, 55.2MiB allocated

Rules

162×	`lower-*.f32`
158×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
110×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	101
0	38	51
1	106	29
0	830	29

Stop Event

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

Counts

14 → 60

Calls

Call 1

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

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

eval26.0ms (0.9%)

Memory: 14.8MiB live, 52.1MiB allocated
Compiler: Compiled 5 010 to 291 computations (94.2% saved)

prune28.0ms (1%)

Memory

-3.9MiB live, 49.1MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	290	4	294
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	292	8	300

Accuracy

100.0%

Counts

300 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	15.7%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
✓	52.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 67 to 39 computations (41.8% saved)

simplify16.0ms (0.6%)

Memory

-20.3MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

360×	`lower-*.f32`
346×	`lower-*.f64`
310×	`associate-r`
308×	`lower-fma.f32`
306×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	164
0	46	151
1	66	131
2	122	115
3	214	109
4	293	109
5	564	109
6	581	109
7	582	109
0	582	106

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize131.0ms (4.6%)

Memory

19.9MiB live, 135.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.06640625	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))
accuracy	0.09994125976844202	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.379258878908963	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)))
accuracy	42.69736909754012	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.33041000976844204	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.4505462890737681	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.42578125	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

79.0ms

256×

valid

Compiler

Compiled 144 to 25 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-div: 30.0ms (47.5% of total)

ival-mult: 12.0ms (19% of total)

ival-sqrt: 8.0ms (12.7% of total)

ival-hypot: 5.0ms (7.9% of total)

ival-exp: 3.0ms (4.8% of total)

ival-log: 3.0ms (4.8% of total)

ival-add: 2.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series14.0ms (0.5%)

Memory

-17.3MiB live, 19.1MiB allocated

Counts

14 → 120

Calls

Call 1

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

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor 0 x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor 0 x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (patch (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 6)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) (patch (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

6.0ms

-inf

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (* (sqrt x) (sqrt 2)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x)) (log 2) (sqrt 2))

2.0ms

inf

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (* (sqrt x) (sqrt 2)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x)) (log 2) (sqrt 2))

2.0ms

((exp (* (log 2) 1/2)) (sqrt (+ (* x x) (* x x))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (* (sqrt x) (sqrt (+ x x))) (sqrt x) (sqrt (+ x x)) (* (sqrt x) (sqrt 2)) (+ (* (* x x) (* x x)) 0) (/ (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x))) (* (+ (* (* x x) (* x x)) 0) (* (+ x x) x)) (log 2) (sqrt 2))

simplify139.0ms (4.8%)

Memory

20.7MiB live, 57.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 858×	`associate-r`
1 460×	`lower-*.f64`
1 460×	`lower-*.f32`
1 456×	`lower-fma.f64`
1 456×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	548
1	71	548
2	211	548
3	453	548
4	848	548
5	1279	548
6	1836	548
7	2171	548
8	2281	548
9	2309	548
10	2329	548
11	2631	548
12	2767	548
13	2767	548
14	2767	548
15	2767	548
16	2767	548
17	3074	548
18	3943	548
19	3951	548
0	3951	548

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 120

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

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

rewrite79.0ms (2.7%)

Memory

18.8MiB live, 56.7MiB allocated

Rules

2 348×	`lower-fma.f32`
2 346×	`lower-fma.f64`
1 632×	`lower-*.f32`
1 626×	`lower-*.f64`
978×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	132
0	46	71
1	117	53
2	770	32
3	4847	32
0	8253	32

Stop Event

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

Counts

14 → 166

Calls

Call 1

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

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

eval79.0ms (2.8%)

Memory: -23.2MiB live, 58.6MiB allocated
Compiler: Compiled 5 839 to 674 computations (88.5% saved)

prune32.0ms (1.1%)

Memory

-2.5MiB live, 69.9MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	308	4	312
Fresh	0	0	0
Picked	2	2	4
Done	0	4	4
Total	310	10	320

Accuracy

100.0%

Counts

320 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	15.8%	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
▶	15.7%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
▶	15.7%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
✓	52.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 116 to 62 computations (46.6% saved)

simplify156.0ms (5.4%)

Memory

-10.3MiB live, 198.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	1344	(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (*.f64 x x)))
cost-diff	0	(.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	1600	(.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x))
cost-diff	0	(.f64 (.f64 (*.f64 x x) x) x)
cost-diff	0	(.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x)))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))

Rules

6 350×	`lower-fma.f64`
6 350×	`lower-fma.f32`
5 934×	`lower-*.f32`
5 912×	`lower-*.f64`
2 740×	`lower-hypot.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	377
0	64	323
1	105	263
2	305	213
3	879	193
4	1416	193
5	3764	193
6	4818	191
7	7423	191
0	8206	188

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
#s(literal 2 binary64)
x
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x)))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x))
(.f64 (.f64 (*.f64 x x) x) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
(*.f64 (+.f64 x x) x)
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)))
(.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))
(.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x))
(.f64 (.f64 (sqrt.f64 x) x) x)
(*.f64 (sqrt.f64 x) x)
(sqrt.f64 x)
x
(*.f64 (+.f64 x x) x)
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))
(*.f64 x x)
(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(.f64 (.f64 (.f64 x x) x) (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 x x)
(*.f64 (+.f64 x x) x)
(+.f64 x x)
#s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))

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

localize111.0ms (3.9%)

Memory

33.1MiB live, 227.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 x x) x)
accuracy	1.9165385448829395	(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (*.f64 x x)))
accuracy	9.379258878908963	(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x)))
accuracy	42.69736909754012	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0.09765625	(.f64 (.f64 (sqrt.f64 x) x) x)
accuracy	0.15234375	(*.f64 (sqrt.f64 x) x)
accuracy	9.379258878908963	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)))
accuracy	42.69736909754012	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0.06640625	(.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x))
accuracy	0.08203125	(.f64 (.f64 x x) x)
accuracy	9.379258878908963	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x)))
accuracy	42.69736909754012	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
accuracy	0.42578125	(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))

Samples

69.0ms

256×

valid

Compiler

Compiled 347 to 36 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 22.0ms (43.2% of total)

ival-sqrt: 8.0ms (15.7% of total)

ival-div: 6.0ms (11.8% of total)

ival-hypot: 5.0ms (9.8% of total)

ival-pow2: 4.0ms (7.8% of total)

ival-pow: 4.0ms (7.8% of total)

ival-add: 2.0ms (3.9% of total)

exact: 1.0ms (2% of total)

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

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

series113.0ms (3.9%)

Memory

-22.0MiB live, 127.7MiB allocated

Counts

19 → 204

Calls

Call 1

Inputs
#s(alt (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (patch (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x)) (patch (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 x x) x) x) (patch (.f64 (.f64 (.f64 x x) x) x) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (patch (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)) (patch (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (patch (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) (patch (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) x) (patch (.f64 (sqrt.f64 x) x) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sqrt.f64 x) x) x) (patch (.f64 (.f64 (sqrt.f64 x) x) x) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (* x x) (* x x))) (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ ( x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x))) (patch (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

78.0ms

((pow (pow 4 1/8) 2) (sqrt (+ (* x x) (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (/ (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (* (* (* (* x x) x) x) (* (+ x x) x)) (* (* (* x x) x) x) (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (/ (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x)) (* (/ 1 x) (* (* (* x x) x) (* x x))) (/ (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x)) (* (* x x) x) (* (sqrt x) x) (* (* (sqrt x) x) x))

14.0ms

inf

((pow (pow 4 1/8) 2) (sqrt (+ (* x x) (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (/ (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (* (* (* (* x x) x) x) (* (+ x x) x)) (* (* (* x x) x) x) (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (/ (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x)) (* (/ 1 x) (* (* (* x x) x) (* x x))) (/ (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x)) (* (* x x) x) (* (sqrt x) x) (* (* (sqrt x) x) x))

12.0ms

-inf

((pow (pow 4 1/8) 2) (sqrt (+ (* x x) (* x x))) (* (pow (pow 4 1/8) 2) x) (pow 4 1/8) (/ (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* x x) x) x) (* (+ x x) x))) (* (* (* (* x x) x) x) (* (+ x x) x)) (* (* (* x x) x) x) (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (/ (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x))) (* (* (* (* (sqrt x) x) x) (* (sqrt x) x)) (* (+ x x) x)) (* (/ 1 x) (* (* (* x x) x) (* x x))) (/ (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (sqrt (+ (* (* x x) (* x x)) 0))) (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x)) (* (* x x) x) (* (sqrt x) x) (* (* (sqrt x) x) x))

simplify111.0ms (3.9%)

Memory

17.3MiB live, 89.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 336×	`lower-*.f64`
1 336×	`lower-fma.f64`
1 336×	`lower-fma.f32`
1 336×	`lower-*.f32`
646×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	940
1	87	940
2	255	940
3	556	940
4	899	940
5	1221	940
6	1524	940
7	2017	940
8	2334	940
9	2460	940
10	2528	940
11	2560	940
12	2578	940
13	2587	940
14	2622	940
15	2636	940
16	2636	940
17	2636	940
18	2785	940
0	2785	940

Stop Event

1×	iter limit
1×	saturated

Counts

204 → 204

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* 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))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (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))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (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))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(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 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(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 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(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 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(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 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* (pow x 3) (sqrt 2))
(.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 3))
(sqrt.f64 (.f64 (.f64 x x) x))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) 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)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 4) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 4 binary64))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (pow x 3) (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (neg.f64 x) x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 #s(literal -2 binary64))))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* -2 (* (pow x 6) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(* -1 (* (pow x 3) (sqrt 2)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) 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)))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 (.f64 x x) x))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 (.f64 x x) x))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 (.f64 x x) x))
(* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(sqrt.f64 (.f64 (.f64 x x) x))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))

rewrite82.0ms (2.8%)

Memory

-2.5MiB live, 117.5MiB allocated

Rules

322×	`lower-*.f32`
304×	`lower-*.f64`
220×	`lower-fma.f64`
220×	`lower-fma.f32`
140×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	275
0	64	192
1	194	72
0	1224	72

Stop Event

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

Counts

19 → 260

Calls

Call 1

Inputs
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x)
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x)))
(.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 (+.f64 x x) x))
(.f64 (.f64 (*.f64 x x) x) x)
(.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x))
(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x)))
(.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (*.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
(sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (*.f64 (+.f64 x x) x))
(.f64 (.f64 x x) x)
(*.f64 (sqrt.f64 x) x)
(.f64 (.f64 (sqrt.f64 x) x) x)

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

eval53.0ms (1.8%)

Memory: 11.3MiB live, 100.8MiB allocated
Compiler: Compiled 9 375 to 528 computations (94.4% saved)

prune28.0ms (1%)

Memory

-11.3MiB live, 66.5MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	498	1	499
Fresh	0	0	0
Picked	1	3	4
Done	0	6	6
Total	499	10	509

Accuracy

100.0%

Counts

509 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	15.8%	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 x x) x) (.f64 x x))) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	15.7%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (sqrt.f64 x) x)) (.f64 (+.f64 x x) x))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
	30.9%	(/.f64 #s(approx (sqrt (* (* (/ 1 x) (* (* (* x x) x) (* x x))) (* (+ x x) x))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x)) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
✓	52.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 308 to 118 computations (61.7% saved)

regimes21.0ms (0.7%)

Memory

4.2MiB live, 43.3MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

regimes17.0ms (0.6%)

Memory

-8.5MiB live, 35.1MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	x
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(*.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 (0.3%)

Memory

19.7MiB live, 19.7MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

regimes6.0ms (0.2%)

Memory

-26.1MiB live, 13.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	x
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
3.8%	1	`x`
3.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.8%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.8%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.2%)

Memory

12.1MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	16	24

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness72.0ms (2.5%)

Memory

-1.4MiB live, 76.6MiB allocated

Rules

162×	`lower-*.f32`
158×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
110×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	22	101
0	38	51
1	106	29
0	830	29

Stop Event

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

Compiler

Compiled 67 to 35 computations (47.8% saved)

preprocess35.0ms (1.2%)

Memory: -9.1MiB live, 68.2MiB allocated
Remove: (abs x)
Compiler: Compiled 68 to 36 computations (47.1% 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	22	136
0	38	122
1	52	110
2	100	95
3	181	89
4	264	89
5	530	89
6	565	89
7	566	89
0	566	89

Iter	Nodes	Cost
0	30	164
0	46	151
1	66	131
2	122	115
3	214	109
4	293	109
5	564	109
6	581	109
7	582	109
0	582	106

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	22	101
0	38	51
1	106	29
0	830	29

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	22	136
0	38	122
1	52	110
2	100	95
3	181	89
4	264	89
5	530	89
6	565	89
7	566	89
0	566	89

Iter	Nodes	Cost
0	30	164
0	46	151
1	66	131
2	122	115
3	214	109
4	293	109
5	564	109
6	581	109
7	582	109
0	582	106

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	22	101
0	38	51
1	106	29
0	830	29

start0.0ms (0%)

analyze0.0ms (0%)

sample938.0ms (32.7%)

explain107.0ms (3.7%)

preprocess19.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize22.0ms (0.8%)

series4.0ms (0.1%)

simplify8.0ms (0.3%)

rewrite32.0ms (1.1%)

eval8.0ms (0.3%)

prune12.0ms (0.4%)

simplify18.0ms (0.6%)

localize62.0ms (2.2%)

series12.0ms (0.4%)

simplify217.0ms (7.6%)

rewrite49.0ms (1.7%)

eval26.0ms (0.9%)

prune28.0ms (1%)

simplify16.0ms (0.6%)

localize131.0ms (4.6%)

series14.0ms (0.5%)

simplify139.0ms (4.8%)

rewrite79.0ms (2.7%)

eval79.0ms (2.8%)

prune32.0ms (1.1%)

simplify156.0ms (5.4%)

localize111.0ms (3.9%)

series113.0ms (3.9%)

simplify111.0ms (3.9%)

rewrite82.0ms (2.8%)

eval53.0ms (1.8%)

prune28.0ms (1%)

regimes21.0ms (0.7%)

regimes17.0ms (0.6%)

regimes8.0ms (0.3%)

regimes6.0ms (0.2%)

simplify5.0ms (0.2%)

soundness72.0ms (2.5%)

preprocess35.0ms (1.2%)

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	22	136
0	38	122
1	52	110
2	100	95
3	181	89
4	264	89
5	530	89
6	565	89
7	566	89
0	566	89

Iter	Nodes	Cost
0	30	164
0	46	151
1	66	131
2	122	115
3	214	109
4	293	109
5	564	109
6	581	109
7	582	109
0	582	106

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	22	101
0	38	51
1	106	29
0	830	29