Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample599.0ms (27.8%)

Memory

25.1MiB live, 807.1MiB allocated

Samples

387.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 243.0ms

ival-pow2: 118.0ms (48.5% of total)

ival-sqrt: 68.0ms (27.9% of total)

ival-add: 48.0ms (19.7% of total)

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

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain71.0ms (3.3%)

Memory

-19.3MiB live, 94.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
130	-	3	(3.397533577224967e-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))))`	uflow-rescue	64	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	64
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	128
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	63	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	63
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	126

Confusion

	Predicted +	Predicted -
+	127	3
-	0	126

Precision

1.0

Recall

0.9769230769230769

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	127	0	3
-	0	0	126

Precision?

1.0

Recall?

0.9769230769230769

Freqs

test

number	freq
0	129
1	127

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 53 to 19 computations (64.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-pow2: 6.0ms (42.1% of total)

ival-sqrt: 5.0ms (35.1% of total)

ival-add: 2.0ms (14% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.8%)

Memory

22.6MiB live, 22.6MiB 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 (+.f64 x 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, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.2%	(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)

simplify8.0ms (0.4%)

Memory

-38.3MiB live, 4.9MiB 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 (+.f64 x x) x))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (+.f64 x x) x)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)

localize16.0ms (0.7%)

Memory

23.1MiB live, 23.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
accuracy	29.963682352233448	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

11.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow2: 3.0ms (48.7% of total)

ival-sqrt: 2.0ms (32.5% of total)

ival-add: 1.0ms (16.2% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.2%)

Memory

5.8MiB live, 5.8MiB 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 (* 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 (* 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 (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 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 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 (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 -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 (* -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

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((pow x 2) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (pow x 2))))

1.0ms

((pow x 2) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (pow x 2))))

1.0ms

-inf

((pow x 2) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (pow x 2))))

simplify5.0ms (0.2%)

Memory

6.2MiB live, 6.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite35.0ms (1.6%)

Memory

4.5MiB live, 42.4MiB 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
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.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 #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 #s(literal 1 binary64) (*.f64 x (+.f64 x x)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.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)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 x x (*.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 0 binary64)) (/.f64 (.f64 (.f64 (.f64 x x) x) x) #s(literal 0 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(.f64 (pow.f64 (.f64 x (+.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 x (+.f64 x x)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 x x))) #s(literal 1/2 binary64)))

eval12.0ms (0.6%)

Memory: -18.0MiB live, 19.8MiB allocated
Compiler: Compiled 774 to 103 computations (86.7% saved)

prune9.0ms (0.4%)

Memory

18.6MiB live, 18.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Accuracy

100.0%

Counts

88 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	17.2%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))))
▶	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	53.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 100 to 50 computations (50% saved)

simplify230.0ms (10.7%)

Memory

-24.4MiB live, 92.9MiB 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	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
cost-diff	5312	(hypot.f64 x x)

Rules

2 560×	`lower-fma.f32`
2 558×	`lower-fma.f64`
1 984×	`lower-*.f32`
1 974×	`lower-*.f64`
1 226×	`unsub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	149
0	38	125
1	57	105
2	118	98
3	215	92
4	301	92
5	576	92
6	685	92
7	734	92
8	896	92
9	1379	92
10	2284	92
11	2979	92
12	3143	92
13	3309	92
14	3341	92
15	3765	92
16	3971	92
17	3977	92
18	3977	92
19	3977	92
20	3977	92
21	3997	92
22	4005	92
23	4005	92
24	4005	92
25	4011	92
0	4011	92

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

localize59.0ms (2.7%)

Memory

6.0MiB live, 81.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.109375	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.02233057032397	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	14.650927223198476	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.49702220496416	(/.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	29.963682352233448	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(neg.f64 x)
accuracy	0.43359375	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	29.829060396763886	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.43359375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	32.742611001342006	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.01171875	(hypot.f64 x x)

Samples

45.0ms

256×

valid

Compiler

Compiled 151 to 23 computations (84.8% saved)

Precisions

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

ival-mult: 9.0ms (28.5% of total)

ival-sqrt: 8.0ms (25.3% of total)

ival-hypot: 5.0ms (15.8% of total)

ival-pow2: 4.0ms (12.7% of total)

ival-add: 3.0ms (9.5% of total)

ival-div: 1.0ms (3.2% of total)

ival-neg: 1.0ms (3.2% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.5%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

14 → 156

Calls

Call 1

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

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

2.0ms

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

simplify80.0ms (3.7%)

Memory

-27.0MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Rules

130×	`lower-*.f64`
130×	`lower-fma.f64`
130×	`lower-fma.f32`
130×	`lower-*.f32`
66×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	636
1	32	636
2	66	636
3	116	636
4	144	636
5	190	636
6	225	636
7	277	636
8	293	636
9	293	636
0	293	636

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

Calls

Call 1

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

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

rewrite49.0ms (2.3%)

Memory

21.2MiB live, 59.9MiB allocated

Rules

178×	`lower-*.f32`
172×	`lower-*.f64`
140×	`lower-fma.f32`
138×	`lower-fma.f64`
104×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	114
0	38	59
1	117	38
0	876	38

Stop Event

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

Counts

14 → 75

Calls

Call 1

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

eval40.0ms (1.9%)

Memory: -12.7MiB live, 58.8MiB allocated
Compiler: Compiled 5 054 to 307 computations (93.9% saved)

prune28.0ms (1.3%)

Memory

6.1MiB live, 55.9MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	296	9	305

Accuracy

100.0%

Counts

305 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	18.3%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
▶	17.2%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	53.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	52.9%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 156 to 91 computations (41.7% saved)

simplify220.0ms (10.2%)

Memory

-2.4MiB live, 73.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
cost-diff	0	(.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	(neg.f64 x)
cost-diff	0	(.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.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

2 560×	`lower-fma.f32`
2 558×	`lower-fma.f64`
1 988×	`lower-*.f32`
1 972×	`lower-*.f64`
1 226×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	241
0	48	208
1	77	164
2	148	152
3	235	140
4	319	140
5	586	140
6	695	140
7	761	140
8	924	140
9	1418	140
10	2327	140
11	3025	140
12	3194	140
13	3360	140
14	3392	140
15	3816	140
16	4022	140
17	4028	140
18	4028	140
19	4028	140
20	4028	140
21	4048	140
22	4056	140
23	4056	140
24	4056	140
25	4062	140
0	4062	134

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize148.0ms (6.9%)

Memory

-6.1MiB live, 114.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.43359375	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	32.742611001342006	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.109375	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.02233057032397	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 x (+.f64 x x))))
accuracy	14.650927223198476	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.49702220496416	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
accuracy	0.0703125	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.109375	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	10.02233057032397	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	40.49702220496416	(/.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	0.43359375	(.f64 (neg.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	29.829060396763886	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Samples

68.0ms

256×

valid

Compiler

Compiled 233 to 29 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 15.0ms (39.8% of total)

ival-sqrt: 6.0ms (15.9% of total)

ival-div: 3.0ms (8% of total)

ival-add: 3.0ms (8% of total)

ival-exp: 3.0ms (8% of total)

ival-log: 3.0ms (8% of total)

ival-pow2: 3.0ms (8% of total)

ival-neg: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.5%)

Memory

24.5MiB live, 24.5MiB allocated

Counts

15 → 144

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify14.0ms (0.7%)

Memory

-24.3MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Rules

122×	`lower-*.f64`
122×	`lower-*.f32`
118×	`lower-fma.f64`
118×	`lower-fma.f32`
58×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	624
1	32	624
2	64	624
3	113	624
4	141	624
5	187	624
6	223	624
7	268	624
8	281	624
9	281	624
0	281	624

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

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

rewrite56.0ms (2.6%)

Memory

6.2MiB live, 44.7MiB allocated

Rules

184×	`lower-*.f32`
172×	`lower-*.f64`
140×	`lower-fma.f32`
138×	`lower-fma.f64`
126×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	164
0	48	138
1	148	43
0	940	43

Stop Event

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

Counts

15 → 78

Calls

Call 1

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

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

eval63.0ms (2.9%)

Memory: -5.9MiB live, 36.3MiB allocated
Compiler: Compiled 4 273 to 306 computations (92.8% saved)

prune27.0ms (1.2%)

Memory

-0.1MiB live, 37.4MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	0	0
Picked	2	3	5
Done	0	4	4
Total	270	8	278

Accuracy

100.0%

Counts

278 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	18.3%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (.f64 x x))
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	53.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	52.9%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 64 to 41 computations (35.9% saved)

simplify6.0ms (0.3%)

Memory

9.5MiB live, 9.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

114×	`lower-*.f32`
104×	`lower-*.f64`
66×	`associate-r`
38×	`associate-l`
30×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	69
0	17	69
1	31	59
2	71	45
3	108	39
4	116	39
5	117	39
0	117	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (1.4%)

Memory

14.5MiB live, 51.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 x (+.f64 x x)))
accuracy	0.0703125	(.f64 (.f64 (*.f64 x x) x) x)
accuracy	10.02233057032397	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (*.f64 x (+.f64 x x))))
accuracy	40.49702220496416	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (.f64 x x))

Samples

23.0ms

256×

valid

Compiler

Compiled 71 to 11 computations (84.5% saved)

Precisions

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

ival-mult: 8.0ms (48.3% of total)

ival-add: 5.0ms (30.2% of total)

ival-div: 2.0ms (12.1% of total)

ival-sqrt: 2.0ms (12.1% of total)

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

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

series8.0ms (0.4%)

Memory

-22.6MiB live, 13.2MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

4.0ms

-inf

((/ (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* x x)) (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* (* (* (* x x) x) x) (* x (+ x x))) (* (* (* x x) x) x))

2.0ms

inf

((/ (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* x x)) (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* (* (* (* x x) x) x) (* x (+ x x))) (* (* (* x x) x) x))

1.0ms

((/ (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* x x)) (sqrt (* (* (* (* x x) x) x) (* x (+ x x)))) (* (* (* (* x x) x) x) (* x (+ x x))) (* (* (* x x) x) x))

simplify9.0ms (0.4%)

Memory

21.0MiB live, 21.0MiB 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	224
1	29	224
2	60	224
3	109	224
4	127	224
5	168	224
6	201	224
7	230	224
8	260	224
9	262	224
0	262	224

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

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

rewrite36.0ms (1.7%)

Memory

-19.6MiB live, 36.9MiB allocated

Rules

150×	`lower-*.f32`
140×	`lower-*.f64`
100×	`lower-/.f32`
98×	`lower-/.f64`
52×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	52
0	17	44
1	53	18
0	321	16

Stop Event

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

Counts

4 → 88

Calls

Call 1

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

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

eval16.0ms (0.8%)

Memory: -6.2MiB live, 29.6MiB allocated
Compiler: Compiled 1 866 to 289 computations (84.5% saved)

prune36.0ms (1.7%)

Memory

0.3MiB live, 37.9MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	135	9	144

Accuracy

100.0%

Counts

144 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	12.6%	(/.f64 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x)) (sqrt.f64 (+.f64 x x))) (.f64 x x))
✓	18.3%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x (+.f64 x x)))) (.f64 x x))
✓	53.2%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	53.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	52.9%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 236 to 89 computations (62.3% saved)

regimes17.0ms (0.8%)

Memory

29.7MiB live, 29.7MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

5.0ms	x
4.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
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)

regimes28.0ms (1.3%)

Memory

1.6MiB live, 38.6MiB allocated

Counts

9 → 2

Calls

Call 1

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

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

Calls

4 calls:

17.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	x
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
3.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
77.7%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
77.7%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
77.7%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes15.0ms (0.7%)

Memory

-22.8MiB live, 18.0MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

9.0ms	x
2.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
48.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
48.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
48.5%	1	`(pow.f64 x #s(literal 2 binary64))`
48.5%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes5.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB 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:

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

Results

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch14.0ms (0.7%)

Memory

-11.5MiB live, 26.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.2684445811105921e-301	3.791511519670732e-307

Samples

6.0ms

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 (59.2% of total)

ival-add: 1.0ms (29.6% of total)

ival-sqrt: 1.0ms (29.6% of total)

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

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

simplify6.0ms (0.3%)

Memory

15.9MiB live, 15.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-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	16	48
1	23	48
2	30	48
3	35	48
4	38	48
5	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))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#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))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(literal 0 binary64)

soundness84.0ms (3.9%)

Memory

-20.0MiB live, 140.5MiB allocated

Rules

178×	`lower-*.f32`
172×	`lower-*.f64`
140×	`lower-fma.f32`
138×	`lower-fma.f64`
104×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	114
0	38	59
1	117	38
0	876	38
0	5	18
0	8	14
1	28	10
0	170	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 70 to 39 computations (44.3% saved)

preprocess30.0ms (1.4%)

Memory: 20.4MiB live, 94.2MiB allocated
Compiler: Compiled 68 to 32 computations (52.9% 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	16	636
1	32	636
2	66	636
3	116	636
4	144	636
5	190	636
6	225	636
7	277	636
8	293	636
9	293	636
0	293	636

Iter	Nodes	Cost
0	17	624
1	32	624
2	64	624
3	113	624
4	141	624
5	187	624
6	223	624
7	268	624
8	281	624
9	281	624
0	281	624

Iter	Nodes	Cost
0	15	224
1	29	224
2	60	224
3	109	224
4	127	224
5	168	224
6	201	224
7	230	224
8	260	224
9	262	224
0	262	224

Iter	Nodes	Cost
0	22	114
0	38	59
1	117	38
0	876	38
0	5	18
0	8	14
1	28	10
0	170	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Iter	Nodes	Cost
0	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	16	636
1	32	636
2	66	636
3	116	636
4	144	636
5	190	636
6	225	636
7	277	636
8	293	636
9	293	636
0	293	636

Iter	Nodes	Cost
0	17	624
1	32	624
2	64	624
3	113	624
4	141	624
5	187	624
6	223	624
7	268	624
8	281	624
9	281	624
0	281	624

Iter	Nodes	Cost
0	15	224
1	29	224
2	60	224
3	109	224
4	127	224
5	168	224
6	201	224
7	230	224
8	260	224
9	262	224
0	262	224

Iter	Nodes	Cost
0	22	114
0	38	59
1	117	38
0	876	38
0	5	18
0	8	14
1	28	10
0	170	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

start0.0ms (0%)

analyze0.0ms (0%)

sample599.0ms (27.8%)

explain71.0ms (3.3%)

preprocess17.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.4%)

localize16.0ms (0.7%)

series4.0ms (0.2%)

simplify5.0ms (0.2%)

rewrite35.0ms (1.6%)

eval12.0ms (0.6%)

prune9.0ms (0.4%)

simplify230.0ms (10.7%)

localize59.0ms (2.7%)

series10.0ms (0.5%)

simplify80.0ms (3.7%)

rewrite49.0ms (2.3%)

eval40.0ms (1.9%)

prune28.0ms (1.3%)

simplify220.0ms (10.2%)

localize148.0ms (6.9%)

series11.0ms (0.5%)

simplify14.0ms (0.7%)

rewrite56.0ms (2.6%)

eval63.0ms (2.9%)

prune27.0ms (1.2%)

simplify6.0ms (0.3%)

localize30.0ms (1.4%)

series8.0ms (0.4%)

simplify9.0ms (0.4%)

rewrite36.0ms (1.7%)

eval16.0ms (0.8%)

prune36.0ms (1.7%)

regimes17.0ms (0.8%)

regimes28.0ms (1.3%)

regimes15.0ms (0.7%)

regimes5.0ms (0.2%)

bsearch14.0ms (0.7%)

simplify6.0ms (0.3%)

soundness84.0ms (3.9%)

preprocess30.0ms (1.4%)

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	16	636
1	32	636
2	66	636
3	116	636
4	144	636
5	190	636
6	225	636
7	277	636
8	293	636
9	293	636
0	293	636

Iter	Nodes	Cost
0	17	624
1	32	624
2	64	624
3	113	624
4	141	624
5	187	624
6	223	624
7	268	624
8	281	624
9	281	624
0	281	624

Iter	Nodes	Cost
0	15	224
1	29	224
2	60	224
3	109	224
4	127	224
5	168	224
6	201	224
7	230	224
8	260	224
9	262	224
0	262	224

Iter	Nodes	Cost
0	22	114
0	38	59
1	117	38
0	876	38
0	5	18
0	8	14
1	28	10
0	170	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148