Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample588.0ms (24.1%)

Memory

19.6MiB live, 759.1MiB allocated

Samples

389.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-pow2: 99.0ms (47.7% of total)

ival-sqrt: 60.0ms (28.9% of total)

ival-add: 39.0ms (18.8% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain73.0ms (3%)

Memory

-6.3MiB live, 115.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
124	-	2	(-4.739140339998984e-162)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	65	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	65
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	130
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	57	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	57
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	114

Confusion

	Predicted +	Predicted -
+	122	3
-	0	131

Precision

1.0

Recall

0.976

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	0	3
-	0	0	131

Precision?

1.0

Recall?

0.976

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-sqrt: 6.0ms (39.9% of total)

ival-pow2: 6.0ms (39.9% of total)

ival-add: 2.0ms (13.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess16.0ms (0.6%)

Memory

20.5MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

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))))
(hypot.f64 x x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.1%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify7.0ms (0.3%)

Memory

-34.9MiB live, 3.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-5184	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
cost-diff	192	(+.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))

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

localize16.0ms (0.7%)

Memory

22.5MiB live, 22.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0078125	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
accuracy	28.710000619475718	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

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 (47.3% of total)

ival-sqrt: 2.0ms (31.5% of total)

ival-add: 1.0ms (15.8% 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

5.4MiB live, 5.4MiB 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	@	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))))
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

((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))))

1.0ms

-inf

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

simplify5.0ms (0.2%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

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)))

rewrite33.0ms (1.3%)

Memory

-2.7MiB live, 35.2MiB allocated

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
#<batchref>
#<batchref>
#<batchref>
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eval12.0ms (0.5%)

Memory: -21.9MiB live, 15.7MiB allocated
Compiler: Compiled 693 to 114 computations (83.5% saved)

prune5.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Accuracy

100.0%

Counts

88 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	49.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify12.0ms (0.5%)

Memory

12.5MiB live, 12.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 x x)
cost-diff	-5184	(sqrt.f64 (*.f64 x (+.f64 x x)))
cost-diff	-128	(+.f64 x x)
cost-diff	0	(*.f64 x (+.f64 x x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) 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))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	25	52
1	36	52
2	48	52
3	59	52
4	65	52
5	76	52
6	104	52
7	123	52
8	138	52
9	216	52
10	346	52
11	360	52
12	364	52
0	364	52

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) (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)
#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
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(hypot.f64 x x)
x

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

localize47.0ms (1.9%)

Memory

-25.5MiB live, 54.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(hypot.f64 x x)
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 x (+.f64 x x))
accuracy	28.710000619475718	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.4296875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	32.2898628052697	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(neg.f64 x)
accuracy	0.4296875	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	30.373239791276287	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Samples

35.0ms

256×

valid

Compiler

Compiled 61 to 15 computations (75.4% saved)

Precisions

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

ival-mult: 6.0ms (27.7% of total)

ival-sqrt: 5.0ms (23.1% of total)

ival-hypot: 4.0ms (18.5% of total)

ival-pow2: 3.0ms (13.9% of total)

ival-add: 2.0ms (9.2% of total)

ival-neg: 1.0ms (4.6% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

simplify7.0ms (0.3%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	436
1	19	436
2	33	436
3	37	436
4	45	436
5	56	436
6	67	436
7	89	436
8	100	436
9	100	436
0	100	436

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

rewrite33.0ms (1.3%)

Memory

-7.0MiB live, 30.7MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	57
0	25	46
1	66	42
0	303	42

Stop Event

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

Counts

10 → 111

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval23.0ms (0.9%)

Memory: -1.8MiB live, 35.4MiB allocated
Compiler: Compiled 1 636 to 248 computations (84.8% saved)

prune16.0ms (0.6%)

Memory

31.1MiB live, 31.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	220	7	227

Accuracy

100.0%

Counts

227 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	26.4%	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
▶	3.4%	(sqrt.f64 (+.f64 x x))
✓	55.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	52.1%	#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)))))

Compiler

Compiled 46 to 39 computations (15.2% saved)

simplify212.0ms (8.7%)

Memory

-15.2MiB live, 111.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	320	(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
cost-diff	7168	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
cost-diff	-128	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	97
0	36	86
1	61	77
2	129	73
3	271	69
4	525	69
5	1097	69
6	2182	69
7	2802	69
8	4503	69
9	7953	69
0	8057	63

Stop Event

1×	iter limit
1×	node limit
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)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)

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)
(sqrt.f64 (+.f64 x x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
x
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
(hypot.f64 x x)
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(fma.f64 x x #s(literal 0 binary64))
(*.f64 x x)
#s(literal 0 binary64)

localize87.0ms (3.6%)

Memory

-5.2MiB live, 111.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	0.05078125	(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
accuracy	13.343429085971412	(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
accuracy	20.18886500844867	(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.203125	(.f64 (neg.f64 x) (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	0.484375	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
accuracy	30.373239791276287	#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

43.0ms	132×	0	invalid
27.0ms	124×	0	valid

Compiler

Compiled 93 to 24 computations (74.2% saved)

Precisions

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

ival-pow: 18.0ms (30.7% of total)

ival-mult: 15.0ms (25.5% of total)

ival-log: 8.0ms (13.6% of total)

ival-sqrt: 5.0ms (8.5% of total)

ival-add: 4.0ms (6.8% of total)

ival-exp: 3.0ms (5.1% of total)

ival-pow2: 3.0ms (5.1% of total)

ival-div: 2.0ms (3.4% of total)

exact: 1.0ms (1.7% of total)

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

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

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

series10.0ms (0.4%)

Memory

19.3MiB live, 19.3MiB allocated

Counts

12 → 120

Calls

Call 1

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

2.0ms

-inf

((exp (* (log 2) 1/2)) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x) (sqrt (+ x x)) (+ x x) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (+ (* x x) 0) (* 2 (pow x 3)) (log 2) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))))

2.0ms

((exp (* (log 2) 1/2)) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (exp (* (log 2) 1/2))) (neg x) (sqrt (+ x x)) (+ x x) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (+ (* x x) 0) (* 2 (pow x 3)) (log 2) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))))

simplify19.0ms (0.8%)

Memory

-17.6MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	516
1	46	516
2	97	516
3	156	516
4	176	516
5	221	516
6	265	516
7	315	516
8	373	516
9	382	516
10	382	516
0	382	516

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 120

Calls

Call 1

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

rewrite93.0ms (3.8%)

Memory

15.3MiB live, 98.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	82
0	36	65
1	114	19
2	775	18
3	4034	18
0	8412	18

Stop Event

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

Counts

12 → 356

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)
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x)
(fma.f64 x x #s(literal 0 binary64))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))
(log.f64 #s(literal 2 binary64))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))

Outputs
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eval81.0ms (3.3%)

Memory: 3.8MiB live, 76.8MiB allocated
Compiler: Compiled 6 410 to 1 284 computations (80% saved)

prune17.0ms (0.7%)

Memory

1.2MiB live, 37.0MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	473	3	476
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	475	8	483

Accuracy

100.0%

Counts

483 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	26.4%	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
✓	3.4%	(sqrt.f64 (+.f64 x x))
✓	55.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	52.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	3.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Compiler

Compiled 47 to 42 computations (10.6% saved)

simplify58.0ms (2.4%)

Memory

-20.2MiB live, 30.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
cost-diff	0	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	116
0	34	109
1	53	97
2	107	97
3	204	97
4	236	97
5	246	97
6	284	97
7	305	97
8	322	97
9	499	97
10	969	97
11	1069	97
12	1161	97
13	1240	97
14	1267	97
15	1302	97
16	1324	97
17	1326	97
0	1326	91

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(neg.f64 x)
x
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
#s(literal 2 binary64)
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 2 binary64)
(fma.f64 x x #s(literal 0 binary64))
#s(literal 0 binary64)

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

localize112.0ms (4.6%)

Memory

1.0MiB live, 78.4MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))
accuracy	0	#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
accuracy	28.710000619475718	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
accuracy	42.837587556584474	(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
accuracy	0	(neg.f64 x)
accuracy	0.4296875	(*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
accuracy	30.373239791276287	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
accuracy	61.663102596546	#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Samples

99.0ms

256×

valid

Compiler

Compiled 92 to 24 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-pow2: 36.0ms (40.9% of total)

ival-mult: 31.0ms (35.2% of total)

ival-pow: 12.0ms (13.6% of total)

ival-add: 3.0ms (3.4% of total)

ival-sqrt: 3.0ms (3.4% of total)

ival-div: 2.0ms (2.3% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

series82.0ms (3.4%)

Memory

-16.9MiB live, 106.3MiB allocated

Counts

10 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) (patch (sqrt.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) (patch (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (patch #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #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))) #s(literal 0 binary64)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 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) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor 0 x) (#s(alt (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #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 (pow x 2) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 0 binary64)) (patch (fma.f64 x x #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) (patch (sqrt.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) (patch (sqrt.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) (patch (sqrt.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) (patch (sqrt.f64 (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) (patch (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) (patch (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) (patch (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) (patch (/.f64 #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (patch #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (patch #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (patch #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (patch #s(approx ( (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 4)) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

55.0ms

((sqrt (+ (pow x 2) (pow x 2))) (pow (pow 4 1/8) 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (pow (pow 4 1/8) 2)) (neg x) (+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

9.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (pow (pow 4 1/8) 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (pow (pow 4 1/8) 2)) (neg x) (+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

7.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (pow (pow 4 1/8) 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (pow (pow 4 1/8) 2)) (neg x) (+ (* x x) 0) (sqrt (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0))) (/ (* (* 2 (pow x 3)) x) (+ (* x x) 0)) (* (* 2 (pow x 3)) x) (* (pow x 4) 2))

simplify8.0ms (0.3%)

Memory

11.1MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	468
1	30	468
2	53	468
3	60	468
4	74	468
5	92	468
6	110	468
7	141	468
8	156	468
9	156	468
0	156	468

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

rewrite119.0ms (4.9%)

Memory

2.1MiB live, 122.0MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	101
0	34	79
1	121	42
2	669	39
3	5555	30
0	8222	30

Stop Event

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

Counts

10 → 534

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(neg.f64 x)
(fma.f64 x x #s(literal 0 binary64))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
#s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))

Outputs
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eval79.0ms (3.3%)

Memory: 18.3MiB live, 125.4MiB allocated
Compiler: Compiled 8 656 to 1 559 computations (82% saved)

prune31.0ms (1.3%)

Memory

-14.5MiB live, 66.1MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	641	1	642
Fresh	0	0	0
Picked	1	2	3
Done	0	5	5
Total	642	8	650

Accuracy

100.0%

Counts

650 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	26.4%	(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
✓	3.4%	(sqrt.f64 (+.f64 x x))
✓	55.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	49.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	52.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))))
✓	52.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	3.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Compiler

Compiled 134 to 86 computations (35.8% saved)

regimes80.0ms (3.3%)

Memory

0.1MiB live, 76.6MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))
(sqrt.f64 (+.f64 x 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 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (.f64 x x)))
(sqrt.f64 (/.f64 #s(approx (* (* 2 (pow x 3)) x) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64))))
(sqrt.f64 (/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #s(literal 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)))))
(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:

55.0ms	x
9.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
7.0ms	(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 19 to 13 computations (31.6% saved)

regimes18.0ms (0.7%)

Memory

24.3MiB live, 24.3MiB allocated

Counts

5 → 2

Calls

Call 1

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

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:

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

Results

Accuracy	Segments	Branch
99.3%	2	`x`
78.0%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
78.0%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
78.0%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes28.0ms (1.1%)

Memory

-21.9MiB live, 24.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

16.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	x
3.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
49.2%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
49.2%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
49.2%	1	`(pow.f64 x #s(literal 2 binary64))`
49.2%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes15.0ms (0.6%)

Memory

-10.5MiB live, 25.1MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.7%	1	`(pow.f64 x #s(literal 2 binary64))`
5.5%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes10.0ms (0.4%)

Memory

20.2MiB live, 20.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.7%	1	`(pow.f64 x #s(literal 2 binary64))`
3.7%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch30.0ms (1.2%)

Memory

-14.4MiB live, 59.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
26.0ms	-1.5676609307514507e-303	6.170978050982554e-295

Samples

16.0ms

160×

valid

Compiler

Compiled 121 to 138 computations (-14% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sqrt: 6.0ms (58% of total)

ival-pow2: 3.0ms (29% of total)

ival-add: 1.0ms (9.7% of total)

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

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

bsearch29.0ms (1.2%)

Memory

-20.0MiB live, 42.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	1.0961656231478106e-210	2.6712807973958285e-192

Samples

17.0ms

160×

valid

Compiler

Compiled 71 to 88 computations (-23.9% saved)

Precisions

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

ival-sqrt: 8.0ms (65.6% of total)

ival-pow2: 3.0ms (24.6% of total)

ival-add: 1.0ms (8.2% of total)

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

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

simplify33.0ms (1.3%)

Memory

29.6MiB live, 29.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	75
1	29	75
2	36	75
3	41	75
4	44	75
5	45	75

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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))
(if (<=.f64 x #s(literal 7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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 -20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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))
(if (<=.f64 x #s(literal 7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64)) (sqrt.f64 (+.f64 x x)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(literal 0 binary64))

soundness217.0ms (8.9%)

Memory

5.8MiB live, 118.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
0	25	46
1	66	42
0	303	42
0	5	18
0	8	14
1	28	10
0	170	9
0	22	82
0	36	65
1	114	19
2	775	18
3	4034	18
0	8412	18
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×	node limit
1×	iter limit
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 123 to 91 computations (26% saved)

preprocess73.0ms (3%)

Memory: -18.2MiB live, 63.5MiB allocated
Compiler: Compiled 86 to 48 computations (44.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

Iter	Nodes	Cost
0	15	65
0	25	52
1	36	52
2	48	52
3	59	52
4	65	52
5	76	52
6	104	52
7	123	52
8	138	52
9	216	52
10	346	52
11	360	52
12	364	52
0	364	52

Iter	Nodes	Cost
0	10	436
1	19	436
2	33	436
3	37	436
4	45	436
5	56	436
6	67	436
7	89	436
8	100	436
9	100	436
0	100	436

Iter	Nodes	Cost
0	24	516
1	46	516
2	97	516
3	156	516
4	176	516
5	221	516
6	265	516
7	315	516
8	373	516
9	382	516
10	382	516
0	382	516

Iter	Nodes	Cost
0	16	468
1	30	468
2	53	468
3	60	468
4	74	468
5	92	468
6	110	468
7	141	468
8	156	468
9	156	468
0	156	468

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

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

Iter	Nodes	Cost
0	15	65
0	25	52
1	36	52
2	48	52
3	59	52
4	65	52
5	76	52
6	104	52
7	123	52
8	138	52
9	216	52
10	346	52
11	360	52
12	364	52
0	364	52

Iter	Nodes	Cost
0	10	436
1	19	436
2	33	436
3	37	436
4	45	436
5	56	436
6	67	436
7	89	436
8	100	436
9	100	436
0	100	436

Iter	Nodes	Cost
0	24	516
1	46	516
2	97	516
3	156	516
4	176	516
5	221	516
6	265	516
7	315	516
8	373	516
9	382	516
10	382	516
0	382	516

Iter	Nodes	Cost
0	16	468
1	30	468
2	53	468
3	60	468
4	74	468
5	92	468
6	110	468
7	141	468
8	156	468
9	156	468
0	156	468

start0.0ms (0%)

analyze0.0ms (0%)

sample588.0ms (24.1%)

explain73.0ms (3%)

preprocess16.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.3%)

localize16.0ms (0.7%)

series4.0ms (0.2%)

simplify5.0ms (0.2%)

rewrite33.0ms (1.3%)

eval12.0ms (0.5%)

prune5.0ms (0.2%)

simplify12.0ms (0.5%)

localize47.0ms (1.9%)

series6.0ms (0.2%)

simplify7.0ms (0.3%)

rewrite33.0ms (1.3%)

eval23.0ms (0.9%)

prune16.0ms (0.6%)

simplify212.0ms (8.7%)

localize87.0ms (3.6%)

series10.0ms (0.4%)

simplify19.0ms (0.8%)

rewrite93.0ms (3.8%)

eval81.0ms (3.3%)

prune17.0ms (0.7%)

simplify58.0ms (2.4%)

localize112.0ms (4.6%)

series82.0ms (3.4%)

simplify8.0ms (0.3%)

rewrite119.0ms (4.9%)

eval79.0ms (3.3%)

prune31.0ms (1.3%)

regimes80.0ms (3.3%)

regimes18.0ms (0.7%)

regimes28.0ms (1.1%)

regimes15.0ms (0.6%)

regimes10.0ms (0.4%)

bsearch30.0ms (1.2%)

bsearch29.0ms (1.2%)

simplify33.0ms (1.3%)

soundness217.0ms (8.9%)

preprocess73.0ms (3%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	15	65
0	25	52
1	36	52
2	48	52
3	59	52
4	65	52
5	76	52
6	104	52
7	123	52
8	138	52
9	216	52
10	346	52
11	360	52
12	364	52
0	364	52

Iter	Nodes	Cost
0	10	436
1	19	436
2	33	436
3	37	436
4	45	436
5	56	436
6	67	436
7	89	436
8	100	436
9	100	436
0	100	436

Iter	Nodes	Cost
0	24	516
1	46	516
2	97	516
3	156	516
4	176	516
5	221	516
6	265	516
7	315	516
8	373	516
9	382	516
10	382	516
0	382	516

Iter	Nodes	Cost
0	16	468
1	30	468
2	53	468
3	60	468
4	74	468
5	92	468
6	110	468
7	141	468
8	156	468
9	156	468
0	156	468