Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample560.0ms (22.4%)

Memory

14.5MiB live, 754.1MiB allocated

Samples

361.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-pow2: 93.0ms (41.2% of total)

ival-sqrt: 88.0ms (39% of total)

ival-add: 35.0ms (15.5% of total)

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

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

Bogosity

explain65.0ms (2.6%)

Memory

36.7MiB live, 114.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
121	-	1	(1.1621919947852576e-160)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	60	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	60
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	120
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	60	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	60
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	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

23.0ms

512×

valid

Compiler

Compiled 53 to 19 computations (64.2% saved)

Precisions

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

ival-pow2: 6.0ms (49.3% of total)

ival-sqrt: 3.0ms (24.7% of total)

ival-add: 2.0ms (16.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (0.8%)

Memory

-21.5MiB live, 23.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.2%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.8%)

Memory

-11.8MiB live, 25.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
accuracy	28.080561670399685	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

13.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-add: 3.0ms (36.3% of total)

ival-pow2: 3.0ms (36.3% of total)

ival-sqrt: 2.0ms (24.2% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

9 calls:

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

simplify6.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite36.0ms (1.4%)

Memory

4.9MiB live, 42.7MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

eval12.0ms (0.5%)

Memory: -21.3MiB live, 16.3MiB allocated
Compiler: Compiled 774 to 104 computations (86.6% saved)

prune9.0ms (0.4%)

Memory

19.4MiB live, 19.4MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Accuracy

100.0%

Counts

88 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	17.9%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
	55.9%	(.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)))
▶	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 132 to 62 computations (53% saved)

simplify238.0ms (9.5%)

Memory

4.7MiB live, 84.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize81.0ms (3.2%)

Memory

-8.1MiB live, 109.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.09765625	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.562583257718213	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	14.90025693871949	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	39.59572088152637	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 x (+.f64 x x))
accuracy	28.080561670399685	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.4609375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	32.162738329261735	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.4609375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	30.365498880980713	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.03125	(hypot.f64 x x)

Samples

44.0ms

256×

valid

Compiler

Compiled 153 to 22 computations (85.6% saved)

Precisions

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

ival-sqrt: 8.0ms (25% of total)

ival-mult: 7.0ms (21.8% of total)

ival-hypot: 5.0ms (15.6% of total)

ival-div: 4.0ms (12.5% of total)

ival-pow2: 4.0ms (12.5% of total)

ival-add: 3.0ms (9.4% of total)

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

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.3%)

Memory

10.5MiB live, 10.5MiB allocated

Counts

13 → 144

Calls

Call 1

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

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

Calls

36 calls:

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

simplify16.0ms (0.7%)

Memory

-19.9MiB live, 17.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 144

Calls

Call 1

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

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

rewrite50.0ms (2%)

Memory

20.7MiB live, 58.6MiB allocated

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

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

Counts

13 → 71

Calls

Call 1

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

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

eval28.0ms (1.1%)

Memory: 16.8MiB live, 53.2MiB allocated
Compiler: Compiled 5 055 to 302 computations (94% saved)

prune87.0ms (3.5%)

Memory

-43.9MiB live, 43.3MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	297	7	304

Accuracy

100.0%

Counts

304 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	18.9%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	49.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 56 to 34 computations (39.3% saved)

simplify83.0ms (3.3%)

Memory

1.4MiB live, 77.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

1 048×	`lower-fma.f32`
1 046×	`lower-fma.f64`
836×	`lower-*.f32`
826×	`lower-*.f64`
614×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	116
0	33	102
1	61	82
2	130	76
3	235	70
4	273	70
5	283	70
6	294	70
7	338	70
8	353	70
9	361	70
10	560	70
11	1360	70
12	1488	70
13	1584	70
14	1663	70
15	1690	70
16	1725	70
17	1747	70
18	1749	70
19	1749	70
0	1749	67

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize108.0ms (4.3%)

Memory

15.5MiB live, 97.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.09765625	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.562583257718213	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	39.59572088152637	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.4609375	(.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)))
accuracy	32.162738329261735	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

Samples

87.0ms

256×

valid

Compiler

Compiled 113 to 22 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-pow2: 47.0ms (66.2% of total)

ival-mult: 8.0ms (11.3% of total)

ival-add: 3.0ms (4.2% of total)

ival-exp: 3.0ms (4.2% of total)

ival-log: 3.0ms (4.2% of total)

ival-sqrt: 3.0ms (4.2% of total)

ival-div: 2.0ms (2.8% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

9 → 84

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

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

Calls

21 calls:

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

simplify15.0ms (0.6%)

Memory

-20.9MiB live, 18.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	384
1	29	384
2	60	384
3	107	384
4	126	384
5	167	384
6	201	384
7	230	384
8	260	384
9	262	384
0	262	384

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

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

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

rewrite169.0ms (6.8%)

Memory

5.6MiB live, 127.1MiB allocated

Rules

2 796×	`lower-fma.f32`
2 794×	`lower-fma.f64`
1 798×	`lower-*.f32`
1 794×	`lower-*.f64`
936×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	95
0	33	53
1	110	19
2	804	15
3	5168	15
0	8566	15

Stop Event

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

Counts

9 → 126

Calls

Call 1

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

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

eval24.0ms (0.9%)

Memory: 0.5MiB live, 37.0MiB allocated
Compiler: Compiled 4 471 to 560 computations (87.5% saved)

prune21.0ms (0.8%)

Memory

12.1MiB live, 50.3MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	209	8	217

Accuracy

100.0%

Counts

217 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	18.9%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
▶	19.7%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	49.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 70 to 41 computations (41.4% saved)

simplify145.0ms (5.8%)

Memory

12.7MiB live, 95.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

1 496×	`lower-fma.f64`
1 496×	`lower-fma.f32`
1 280×	`lower-*.f32`
1 264×	`lower-*.f64`
1 122×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	195
0	50	178
1	93	156
2	207	135
3	383	125
4	505	125
5	640	125
6	717	125
7	785	125
8	825	125
9	1249	125
10	2092	125
11	2878	125
12	3028	125
13	3142	125
14	3170	125
15	3182	125
16	3404	125
17	3510	125
18	3510	125
19	3510	125
20	3510	125
21	3514	125
0	3514	122

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize104.0ms (4.2%)

Memory

-32.8MiB live, 130.2MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.08203125	(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	10.562583257718213	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
accuracy	39.59572088152637	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
accuracy	0.09765625	(.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x))))
accuracy	0.22332001953688402	(.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x)))
accuracy	20.74380357083326	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (*.f64 x x)))))
accuracy	39.59572088152637	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
accuracy	0	(neg.f64 (*.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))
accuracy	32.162738329261735	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))))

Samples

61.0ms

256×

valid

Compiler

Compiled 168 to 30 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 14.0ms (30.8% of total)

ival-sqrt: 13.0ms (28.6% of total)

ival-pow2: 5.0ms (11% of total)

ival-pow: 4.0ms (8.8% of total)

ival-div: 3.0ms (6.6% of total)

ival-add: 3.0ms (6.6% of total)

ival-neg: 2.0ms (4.4% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.3%)

Memory

13.9MiB live, 14.0MiB allocated

Counts

13 → 144

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

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

Calls

36 calls:

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

simplify14.0ms (0.6%)

Memory

19.9MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	716
1	37	716
2	79	716
3	111	716
4	129	716
5	167	716
6	199	716
7	230	716
8	261	716
9	261	716
0	261	716

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 144

Calls

Call 1

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

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

rewrite150.0ms (6%)

Memory

7.0MiB live, 201.5MiB allocated

Rules

3 482×	`lower-fma.f64`
3 482×	`lower-fma.f32`
2 384×	`lower-*.f32`
2 378×	`lower-*.f64`
1 284×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	166
0	50	102
1	164	44
2	969	28
3	6300	28
0	8084	28

Stop Event

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

Counts

13 → 405

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 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 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/8 binary64) (log.f64 #s(literal 4 binary64))))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (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 1/16 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 (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))
(neg.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))
(*.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))
#s(literal 0 binary64)
#s(literal 0 binary64)
(exp.f64 (.f64 (log.f64 (.f64 x (/.f64 x #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x x)))
(neg.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x x)))
(/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal -1 binary64))
(/.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))
(/.f64 #s(literal -1 binary64) (*.f64 x (/.f64 x #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)))))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x) x)
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x) (neg.f64 x))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x)) x)
(/.f64 (neg.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))))
(/.f64 (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64)) (.f64 x x))
(/.f64 (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64))) (.f64 x x))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #s(literal -1 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)))) (.f64 x x))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x))) (neg.f64 x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64))) (*.f64 x x))
(/.f64 (*.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x) #s(literal 1 binary64)) x)
(/.f64 (/.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x) (sqrt.f64 x)) (sqrt.f64 x))
(/.f64 (/.f64 (neg.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) x)) #s(literal -1 binary64)) x)
(/.f64 (/.f64 (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64)) (sqrt.f64 x)) (.f64 x (sqrt.f64 x)))
(/.f64 (/.f64 (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64)) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(/.f64 (/.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(/.f64 (/.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(pow.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (*.f64 x (/.f64 x #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x x) (.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (.f64 x x)) #s(literal 1 binary64))
(.f64 (neg.f64 #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
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(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x (.f64 x x))))
(.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (.f64 x (sqrt.f64 x)) (.f64 x (.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (.f64 (.f64 x x) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x))))))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 x (.f64 (.f64 x x) (.f64 x x))))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (sqrt.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) x)
(.f64 (sqrt.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))) (sqrt.f64 x))
(.f64 (/.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x))) x))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) x) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (.f64 x x)))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x))))) x))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 (.f64 x x) (.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (*.f64 x x)))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 (.f64 x x) (*.f64 x x))) x))
(.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 x x) (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (*.f64 x x)) x))
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 (.f64 x x) (.f64 x x)))) x)
(.f64 (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (*.f64 x x)) x))
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) x) x)
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) x) (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (*.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) x) (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) x) (/.f64 (.f64 x x) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) x) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x (.f64 x x))) x)
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))) x))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x x) (.f64 x x))))
(.f64 (/.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(.f64 (/.f64 (.f64 x x) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x)))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 (.f64 x (*.f64 x x)) x))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 x (*.f64 x x)) x))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) (neg.f64 x))
(.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 x (.f64 (.f64 x x) (.f64 x x)))) (/.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (*.f64 x x)) x))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) x) (/.f64 x (.f64 x (*.f64 x x))))
(.f64 (/.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) x) (/.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))
(.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 x (/.f64 #s(literal 1 binary64) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (pow.f64 x #s(literal 24 binary64))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (.f64 (.f64 x x) (.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(.f64 (.f64 (neg.f64 x) (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)))
(.f64 (.f64 (.f64 x (.f64 x x)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x x)))
(+.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) #s(literal 0 binary64))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 6 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))
(fma.f64 x (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) x #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (.f64 x (.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 x)) (.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 x (sqrt.f64 x)) (neg.f64 (.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (sqrt.f64 x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal 9/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 9/4 binary64)) #s(literal 0 binary64))
(fma.f64 (neg.f64 (.f64 x (sqrt.f64 x))) (.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(neg.f64 (.f64 x (.f64 x x)))
(/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x x))) (*.f64 x x))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal 3/8 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -3/4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (.f64 x x) (neg.f64 x))
(.f64 (.f64 x (*.f64 x x)) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))
(.f64 (neg.f64 x) (.f64 x x))
(.f64 (sqrt.f64 x) (.f64 x (*.f64 x (sqrt.f64 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 x (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 9/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 9/4 binary64)))
(.f64 (neg.f64 (.f64 x (sqrt.f64 x))) (*.f64 x (sqrt.f64 x)))

eval66.0ms (2.6%)

Memory: -4.4MiB live, 146.5MiB allocated
Compiler: Compiled 13 877 to 1 627 computations (88.3% saved)

prune72.0ms (2.9%)

Memory

0.6MiB live, 190.2MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	549	0	549
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	549	8	557

Accuracy

100.0%

Counts

557 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	18.9%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
✓	19.7%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (.f64 x x))))) (.f64 x x))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))))
✓	49.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 209 to 83 computations (60.3% saved)

regimes36.0ms (1.4%)

Memory

-0.7MiB live, 51.8MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	x
4.0ms	(pow.f64 x #s(literal 2 binary64))
4.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes15.0ms (0.6%)

Memory

-2.2MiB live, 35.0MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.3%	2	`x`
79.1%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
79.1%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
79.1%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes6.0ms (0.3%)

Memory

18.7MiB live, 18.7MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
52.2%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
52.2%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
52.2%	1	`(pow.f64 x #s(literal 2 binary64))`
52.2%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes8.0ms (0.3%)

Memory

-12.5MiB live, 24.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

4.0ms	x
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
3.9%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.9%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.9%	1	`(pow.f64 x #s(literal 2 binary64))`
3.9%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch17.0ms (0.7%)

Memory

-0.5MiB live, 33.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	-3.106008247552752e-304	7.881650468810217e-308

Samples

10.0ms

144×

valid

Compiler

Compiled 147 to 107 computations (27.2% saved)

Precisions

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

ival-pow2: 2.0ms (61% of total)

ival-add: 1.0ms (30.5% of total)

ival-sqrt: 1.0ms (30.5% of total)

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

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

simplify6.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	23	48
2	32	48
3	37	48
4	39	48

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness138.0ms (5.5%)

Memory

5.9MiB live, 127.9MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated

Compiler

Compiled 70 to 38 computations (45.7% saved)

preprocess44.0ms (1.7%)

Memory: 0.7MiB live, 79.8MiB allocated
Compiler: Compiled 68 to 30 computations (55.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

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

Iter	Nodes	Cost
0	15	384
1	29	384
2	60	384
3	107	384
4	126	384
5	167	384
6	201	384
7	230	384
8	260	384
9	262	384
0	262	384

Iter	Nodes	Cost
0	18	716
1	37	716
2	79	716
3	111	716
4	129	716
5	167	716
6	199	716
7	230	716
8	261	716
9	261	716
0	261	716

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

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

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

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

Iter	Nodes	Cost
0	15	384
1	29	384
2	60	384
3	107	384
4	126	384
5	167	384
6	201	384
7	230	384
8	260	384
9	262	384
0	262	384

Iter	Nodes	Cost
0	18	716
1	37	716
2	79	716
3	111	716
4	129	716
5	167	716
6	199	716
7	230	716
8	261	716
9	261	716
0	261	716

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

start0.0ms (0%)

analyze0.0ms (0%)

sample560.0ms (22.4%)

explain65.0ms (2.6%)

preprocess20.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize20.0ms (0.8%)

series3.0ms (0.1%)

simplify6.0ms (0.2%)

rewrite36.0ms (1.4%)

eval12.0ms (0.5%)

prune9.0ms (0.4%)

simplify238.0ms (9.5%)

localize81.0ms (3.2%)

series7.0ms (0.3%)

simplify16.0ms (0.7%)

rewrite50.0ms (2%)

eval28.0ms (1.1%)

prune87.0ms (3.5%)

simplify83.0ms (3.3%)

localize108.0ms (4.3%)

series4.0ms (0.2%)

simplify15.0ms (0.6%)

rewrite169.0ms (6.8%)

eval24.0ms (0.9%)

prune21.0ms (0.8%)

simplify145.0ms (5.8%)

localize104.0ms (4.2%)

series7.0ms (0.3%)

simplify14.0ms (0.6%)

rewrite150.0ms (6%)

eval66.0ms (2.6%)

prune72.0ms (2.9%)

regimes36.0ms (1.4%)

regimes15.0ms (0.6%)

regimes6.0ms (0.3%)

regimes8.0ms (0.3%)

bsearch17.0ms (0.7%)

simplify6.0ms (0.2%)

soundness138.0ms (5.5%)

preprocess44.0ms (1.7%)

end0.0ms (0%)

Profiling

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

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

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

Iter	Nodes	Cost
0	15	384
1	29	384
2	60	384
3	107	384
4	126	384
5	167	384
6	201	384
7	230	384
8	260	384
9	262	384
0	262	384

Iter	Nodes	Cost
0	18	716
1	37	716
2	79	716
3	111	716
4	129	716
5	167	716
6	199	716
7	230	716
8	261	716
9	261	716
0	261	716

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