Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample839.0ms (20.3%)

Memory

-3.8MiB live, 521.1MiB allocated

Samples

666.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 188.0ms

ival-hypot: 179.0ms (95.4% of total)

ival-true: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain90.0ms (2.2%)

Memory

0.8MiB live, 119.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
121	-	1	(1.1621919947852576e-160)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	60	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	60
↳	`(*.f64 x x)`	underflow	120
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	60	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	60
↳	`(*.f64 x x)`	overflow	120

Confusion

	Predicted +	Predicted -
+	120	1
-	0	135

Precision

1.0

Recall

0.9917355371900827

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	1
-	0	0	135

Precision?

1.0

Recall?

0.9917355371900827

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

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

ival-hypot: 8.0ms (46.6% of total)

ival-mult: 6.0ms (34.9% of total)

ival-add: 2.0ms (11.6% of total)

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

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

preprocess17.0ms (0.4%)

Memory

-9.6MiB live, 28.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

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

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB 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 x (+.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 x x)
x

localize20.0ms (0.5%)

Memory

6.7MiB live, 43.6MiB 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	28.080561670399685	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

15.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-hypot: 5.0ms (68.1% of total)

ival-mult: 2.0ms (27.2% of total)

ival-add: 1.0ms (13.6% of total)

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

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

series6.0ms (0.2%)

Memory

-28.0MiB live, 7.1MiB 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 (* 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 (* 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 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 (* 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 (* -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 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 (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 (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

9 calls:

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

simplify6.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite39.0ms (0.9%)

Memory

-10.7MiB live, 41.1MiB 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) (.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)) (/.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)))
(fma.f64 x x (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))))
(*.f64 x (+.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(*.f64 (+.f64 x x) x)
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x x))) #s(literal 1/2 binary64)))
(hypot.f64 x x)
(hypot.f64 x (pow.f64 x #s(literal 1 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) x)
(hypot.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (+.f64 x x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (pow.f64 (.f64 x (+.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))

eval11.0ms (0.3%)

Memory: -5.8MiB live, 31.5MiB allocated
Compiler: Compiled 750 to 94 computations (87.5% saved)

prune7.0ms (0.2%)

Memory

20.0MiB live, 20.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Accuracy

100.0%

Counts

86 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 25 to 15 computations (40% saved)

simplify5.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

22×	`lower-*.f32`
16×	`lower-*.f64`
10×	`*-commutative`
8×	`lift-sqrt.f64`
8×	`lower-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	52
0	23	49
1	28	49
2	31	49
0	31	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize80.0ms (1.9%)

Memory

-33.1MiB live, 126.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.03125	(hypot.f64 x x)
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.3951950195368841	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	28.080561670399685	(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 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.4609375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

Samples

31.0ms

256×

valid

Compiler

Compiled 59 to 13 computations (78% saved)

Precisions

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

ival-sqrt: 8.0ms (35.6% of total)

ival-hypot: 6.0ms (26.7% of total)

ival-add: 4.0ms (17.8% of total)

ival-mult: 4.0ms (17.8% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

simplify139.0ms (3.4%)

Memory

18.1MiB live, 94.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 478×	`associate-r`
1 232×	`lower-*.f64`
1 232×	`lower-fma.f64`
1 232×	`lower-fma.f32`
1 232×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	464
1	50	464
2	136	464
3	265	464
4	490	464
5	809	464
6	1411	464
7	1537	464
8	1592	464
9	1630	464
10	1808	464
11	2022	464
12	2068	464
13	2096	464
14	2100	464
15	2100	464
16	2246	464
17	2430	464
18	3585	464
19	3703	464
20	3727	464
21	3735	464
22	3739	464
23	3743	464
24	3855	464
25	3903	464
26	3903	464
27	4085	464
0	4085	464

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

rewrite42.0ms (1%)

Memory

-8.0MiB live, 71.3MiB allocated

Rules

98×	`lower-*.f32`
92×	`lower-*.f64`
68×	`lower-fma.f64`
68×	`lower-fma.f32`
58×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
0	23	38
1	51	34
0	255	34

Stop Event

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

Counts

10 → 127

Calls

Call 1

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

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

eval28.0ms (0.7%)

Memory: -3.7MiB live, 68.2MiB allocated
Compiler: Compiled 2 492 to 231 computations (90.7% saved)

prune26.0ms (0.6%)

Memory

22.4MiB live, 63.8MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	269	4	273
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	269	8	277

Accuracy

100.0%

Counts

277 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	36.0%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	7.0%	(sqrt.f64 (+.f64 x x))
▶	23.6%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 85 to 47 computations (44.7% saved)

simplify203.0ms (4.9%)

Memory

-8.6MiB live, 381.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	832	(sqrt.f64 (fma.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 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
cost-diff	64	(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
cost-diff	1216	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x))))
cost-diff	2432	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

10 370×	`lower-fma.f32`
10 366×	`lower-fma.f64`
6 196×	`lower-*.f32`
6 180×	`lower-*.f64`
1 378×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	240
0	52	220
1	91	125
2	245	115
3	1379	115
4	3711	115
5	5568	115
0	8001	109

Stop Event

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

Calls

Call 1

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

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

localize95.0ms (2.3%)

Memory

27.5MiB live, 220.3MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.3951950195368841	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
accuracy	19.427161526458804	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
accuracy	19.491427890169096	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64))))
accuracy	28.019773927468947	(sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x))))
accuracy	28.080561670399685	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
accuracy	47.08906479255915	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
accuracy	0.4609375	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

54.0ms

256×

valid

Compiler

Compiled 252 to 30 computations (88.1% saved)

Precisions

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

ival-mult: 13.0ms (33.2% of total)

ival-sqrt: 7.0ms (17.9% of total)

ival-hypot: 5.0ms (12.8% of total)

ival-div: 4.0ms (10.2% of total)

ival-add: 4.0ms (10.2% of total)

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

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

exact: 1.0ms (2.6% of total)

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

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

series32.0ms (0.8%)

Memory

-19.8MiB live, 20.6MiB allocated

Counts

18 → 180

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

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

Calls

45 calls:

Time	Variable		Point	Expression
22.0ms	x	@	inf	(/ 1 (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))))
0.0ms	x	@	-inf	(/ 1 (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))))
0.0ms	x	@	0	(/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x)))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	-inf	(* x (* x x))

simplify265.0ms (6.4%)

Memory

0.9MiB live, 117.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 728×	`lower-*.f64`
1 728×	`lower-fma.f64`
1 728×	`lower-fma.f32`
1 728×	`lower-*.f32`
1 500×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	720
1	65	720
2	156	720
3	284	720
4	516	720
5	837	720
6	1377	720
7	1566	720
8	1717	720
9	1811	720
10	1895	720
11	1960	720
12	1986	720
13	1997	720
14	1998	720
15	1998	720
16	2150	720
17	2944	720
18	3242	720
19	3785	720
20	4033	720
21	4791	720
22	5199	720
23	5621	720
24	5765	720
25	5777	720
26	5777	720
27	5797	720
28	5831	720
29	5833	720
30	5833	720
31	5913	720
32	5945	720
33	5945	720
34	6063	720
35	6441	720
36	6465	720
0	6465	720

Stop Event

1×	iter limit
1×	saturated

Counts

180 → 172

Calls

Call 1

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

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

rewrite184.0ms (4.5%)

Memory

-27.4MiB live, 325.0MiB allocated

Rules

3 834×	`lower-fma.f32`
3 830×	`lower-fma.f64`
2 306×	`lower-*.f32`
2 300×	`lower-*.f64`
1 208×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	177
0	52	92
1	167	36
2	1455	32
3	6159	32
0	8376	32

Stop Event

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

Counts

18 → 610

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

Outputs
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
#s(literal 0 binary64)
#s(literal 0 binary64)
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(exp.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -4 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 x) (.f64 #s(literal 1/2 binary64) (log.f64 x))) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) x #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
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(/.f64 (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) x) (.f64 x (.f64 x x)))
(/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -3/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -3/2 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))) #s(literal -1 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) x))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))) x))
(.f64 (.f64 x (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(.f64 (.f64 x (sqrt.f64 x)) (neg.f64 (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 x (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 x (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 x (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 x (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))) x))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) x))
(.f64 (neg.f64 (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
#s(literal 0 binary64)
#s(literal 0 binary64)

eval153.0ms (3.7%)

Memory: 26.7MiB live, 250.2MiB allocated
Compiler: Compiled 43 702 to 4 897 computations (88.8% saved)

prune253.0ms (6.1%)

Memory

-27.4MiB live, 221.9MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 266	5	1 271
Fresh	0	0	0
Picked	3	1	4
Done	0	4	4
Total	1 269	10	1 279

Accuracy

100.0%

Counts

1 279 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	36.0%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))))
▶	39.4%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.0%	(sqrt.f64 (+.f64 x x))
▶	56.1%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	3.9%	#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))

Compiler

Compiled 146 to 92 computations (37% saved)

simplify335.0ms (8.1%)

Memory

42.1MiB live, 342.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	1344	(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x)
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	0	#s(approx (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))
cost-diff	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
cost-diff	0	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
cost-diff	12288	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Rules

10 774×	`lower-fma.f32`
10 772×	`lower-fma.f64`
9 106×	`lower-*.f32`
9 094×	`lower-*.f64`
2 606×	`distribute-lft-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	302
0	57	250
1	98	164
2	279	161
3	1229	161
4	2590	161
5	3303	161
6	4245	161
7	5693	161
8	6070	161
9	6233	161
10	6330	161
11	6432	161
12	6544	161
0	8369	155

Stop Event

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

Calls

Call 1

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

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

localize138.0ms (3.3%)

Memory

-20.5MiB live, 195.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.3951950195368841	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))))
accuracy	19.427161526458804	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
accuracy	19.491427890169096	(/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x)))
accuracy	28.17993026638233	(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))
accuracy	0.1015625	(*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))
accuracy	0.3951950195368841	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x))
accuracy	19.427161526458804	(sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)))
accuracy	19.491427890169096	(/.f64 (sqrt.f64 (*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x)
accuracy	0	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x)
accuracy	0	#s(approx (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) #s(approx (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x)))
accuracy	28.080561670399685	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x))
accuracy	61.52823721024244	#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))
accuracy	0	(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
accuracy	0.4609375	(*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Samples

65.0ms

256×

valid

Compiler

Compiled 288 to 33 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 13.0ms (27.2% of total)

ival-div: 9.0ms (18.9% of total)

ival-hypot: 7.0ms (14.7% of total)

ival-pow2: 7.0ms (14.7% of total)

ival-sqrt: 5.0ms (10.5% of total)

ival-pow: 4.0ms (8.4% of total)

ival-add: 3.0ms (6.3% of total)

exact: 1.0ms (2.1% of total)

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

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

series32.0ms (0.8%)

Memory

-20.8MiB live, 17.8MiB allocated

Counts

18 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

simplify369.0ms (8.9%)

Memory

24.8MiB live, 179.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2 176×	`lower-*.f64`
2 176×	`lower-fma.f64`
2 176×	`lower-fma.f32`
2 176×	`lower-*.f32`
1 970×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	828
1	57	828
2	117	828
3	157	828
4	366	828
5	897	828
6	1210	828
7	1570	828
8	1902	828
9	2017	828
10	2092	828
11	2230	828
12	2367	828
13	2415	828
14	2430	828
15	2431	828
16	2431	828
17	2565	828
18	2817	828
19	2945	828
20	3123	828
21	3340	828
22	4047	828
23	4447	828
24	4723	828
25	4867	828
26	4911	828
27	4911	828
28	4931	828
29	4959	828
30	4961	828
31	4961	828
32	5353	828
33	6084	828
34	6600	828
35	6648	828
36	6648	828
37	6702	828
38	6720	828
39	6720	828
40	6720	828
41	6992	828
42	7651	828
43	7659	828
0	7659	828

Stop Event

1×	iter limit
1×	saturated

Counts

192 → 180

Calls

Call 1

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

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

rewrite150.0ms (3.6%)

Memory

10.0MiB live, 242.6MiB allocated

Rules

2 740×	`lower-fma.f32`
2 738×	`lower-fma.f64`
2 534×	`lower-*.f32`
2 528×	`lower-*.f64`
1 622×	`lower-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	252
0	57	164
1	202	43
2	1672	43
3	7654	43
0	8625	43

Stop Event

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

Counts

18 → 604

Calls

Call 1

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

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

eval133.0ms (3.2%)

Memory: 11.1MiB live, 241.0MiB allocated
Compiler: Compiled 23 123 to 2 434 computations (89.5% saved)

prune115.0ms (2.8%)

Memory

-16.0MiB live, 258.4MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	1 018	2	1 020
Fresh	0	0	0
Picked	2	3	5
Done	0	5	5
Total	1 020	10	1 030

Accuracy

100.0%

Counts

1 030 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	36.0%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (.f64 x x) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))))
	39.4%	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (*.f64 x x) (+.f64 x x))) x))
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.0%	(sqrt.f64 (+.f64 x x))
✓	56.1%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x))
✓	56.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	3.9%	#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))

Compiler

Compiled 257 to 106 computations (58.8% saved)

regimes24.0ms (0.6%)

Memory

16.8MiB live, 51.0MiB allocated

Counts

16 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

9.0ms	(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)

regimes18.0ms (0.4%)

Memory

-2.2MiB live, 36.8MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))
(sqrt.f64 (+.f64 x x))
#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (+ ( x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))) (/.f64 #s(literal 1/2 binary64) x))) x))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (*.f64 x x) (+.f64 x x))) x))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) x))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (sqrt.f64 (fma.f64 x x #s(literal 0 binary64)))))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (.f64 x x) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))))
(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x 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 x x)
4.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.4%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.4%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes9.0ms (0.2%)

Memory

18.2MiB live, 18.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes7.0ms (0.2%)

Memory

-26.0MiB live, 13.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
7.0%	1	`x`
7.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
7.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
7.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(literal 0 binary64))

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	17	37

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

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

soundness189.0ms (4.6%)

Memory

-2.7MiB live, 154.6MiB allocated

Rules

3 834×	`lower-fma.f32`
3 830×	`lower-fma.f64`
2 306×	`lower-*.f32`
2 300×	`lower-*.f64`
1 208×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	177
0	52	92
1	167	36
2	1455	32
3	6159	32
0	8376	32
0	15	44
0	23	38
1	51	34
0	255	34
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 101 to 54 computations (46.5% saved)

preprocess54.0ms (1.3%)

Memory: -28.3MiB live, 86.2MiB allocated
Remove: (abs x)
Compiler: Compiled 70 to 32 computations (54.3% 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	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

start0.0ms (0%)

analyze0.0ms (0%)

sample839.0ms (20.3%)

explain90.0ms (2.2%)

preprocess17.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize20.0ms (0.5%)

series6.0ms (0.2%)

simplify6.0ms (0.1%)

rewrite39.0ms (0.9%)

eval11.0ms (0.3%)

prune7.0ms (0.2%)

simplify5.0ms (0.1%)

localize80.0ms (1.9%)

series6.0ms (0.2%)

simplify139.0ms (3.4%)

rewrite42.0ms (1%)

eval28.0ms (0.7%)

prune26.0ms (0.6%)

simplify203.0ms (4.9%)

localize95.0ms (2.3%)

series32.0ms (0.8%)

simplify265.0ms (6.4%)

rewrite184.0ms (4.5%)

eval153.0ms (3.7%)

prune253.0ms (6.1%)

simplify335.0ms (8.1%)

localize138.0ms (3.3%)

series32.0ms (0.8%)

simplify369.0ms (8.9%)

rewrite150.0ms (3.6%)

eval133.0ms (3.2%)

prune115.0ms (2.8%)

regimes24.0ms (0.6%)

regimes18.0ms (0.4%)

regimes9.0ms (0.2%)

regimes7.0ms (0.2%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness189.0ms (4.6%)

preprocess54.0ms (1.3%)

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