Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample587.0ms (27.7%)

Memory

32.6MiB live, 766.4MiB allocated

Samples

385.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 236.0ms

ival-pow2: 106.0ms (44.9% of total)

ival-sqrt: 81.0ms (34.3% of total)

ival-add: 40.0ms (16.9% of total)

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

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

Bogosity

explain74.0ms (3.5%)

Memory

-25.8MiB live, 93.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
144	0	-	144	(1.1437867450522786e-219)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	51	(3.0425546302133684e+195)	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	nan-rescue	51	0
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	71
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	71

Confusion

	Predicted +	Predicted -
+	31	113
-	20	92

Precision

0.6078431372549019

Recall

0.2152777777777778

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	31	0	113
-	20	0	92

Precision?

0.6078431372549019

Recall?

0.2152777777777778

Freqs

test

number	freq
0	205
1	51

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 92 to 39 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow2: 6.0ms (47.3% of total)

ival-sqrt: 4.0ms (31.5% of total)

ival-add: 2.0ms (15.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess16.0ms (0.8%)

Memory

20.9MiB live, 20.9MiB 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)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.0%	(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)

simplify3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB 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)

localize21.0ms (1%)

Memory

-14.1MiB live, 23.5MiB 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	33.29153900986449	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

16.0ms

256×

valid

Compiler

Compiled 42 to 12 computations (71.4% saved)

Precisions

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

ival-pow2: 3.0ms (48.8% of total)

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

ival-add: 1.0ms (16.3% 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

5.6MiB live, 5.6MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

5.7MiB live, 5.7MiB 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 (1.6%)

Memory

-5.7MiB live, 31.9MiB 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>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval8.0ms (0.4%)

Memory: 14.0MiB live, 14.0MiB allocated
Compiler: Compiled 693 to 114 computations (83.5% saved)

prune10.0ms (0.5%)

Memory

-23.5MiB live, 14.9MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Accuracy

100.0%

Counts

88 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	17.5%	(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
▶	48.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	55.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 64 to 56 computations (12.5% saved)

simplify13.0ms (0.6%)

Memory

14.2MiB live, 14.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
cost-diff	0	(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
cost-diff	0	(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
cost-diff	192	(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
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	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
cost-diff	0	(hypot.f64 x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	109
0	40	90
1	56	90
2	72	90
3	83	90
4	89	90
5	100	90
6	128	90
7	147	90
8	162	90
9	241	90
10	380	90
11	395	90
12	400	90
0	400	90

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

Outputs
(hypot.f64 x x)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(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)
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

localize94.0ms (4.4%)

Memory

-7.3MiB live, 87.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
accuracy	33.29153900986449	(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
accuracy	48.440238902944294	(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 x (+.f64 x x))
accuracy	33.29153900986449	(sqrt.f64 (*.f64 x (+.f64 x x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	(neg.f64 x)
accuracy	0.46484375	(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	28.48685978822495	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.46484375	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	34.03563358549369	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.015625	(hypot.f64 x x)

Samples

77.0ms

256×

valid

Compiler

Compiled 198 to 45 computations (77.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-pow: 36.0ms (55.9% of total)

ival-sqrt: 9.0ms (14% of total)

ival-mult: 6.0ms (9.3% of total)

ival-hypot: 5.0ms (7.8% of total)

ival-add: 3.0ms (4.7% of total)

ival-div: 2.0ms (3.1% of total)

ival-pow2: 2.0ms (3.1% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.6%)

Memory

-19.4MiB live, 18.6MiB allocated

Counts

14 → 156

Calls

Call 1

Inputs
#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt (.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 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))) (patch (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) #<representation binary64>) () ())

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))
2.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))

Time

Variable

Point

Expression

2.0ms

inf

((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))

2.0ms

-inf

((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))

2.0ms

((sqrt (+ (* x x) (* x x))) (sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* (neg x) (sqrt 2)) (neg x) (* x (+ x x)) (+ x x) (sqrt (* x (+ x x))) (+ 0 (pow x 4)) (sqrt (/ (* 2 (pow x 6)) (+ 0 (pow x 4)))) (/ (* 2 (pow x 6)) (+ 0 (pow x 4))) (* 2 (pow x 6)))

simplify7.0ms (0.3%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	644
1	25	644
2	39	644
3	43	644
4	51	644
5	62	644
6	73	644
7	95	644
8	106	644
9	106	644
0	106	644

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

Calls

Call 1

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

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

rewrite44.0ms (2.1%)

Memory

8.2MiB live, 46.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	90
0	40	56
1	122	56
0	707	56

Stop Event

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

Counts

14 → 346

Calls

Call 1

Inputs
(hypot.f64 x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(*.f64 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))

Outputs
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eval47.0ms (2.2%)

Memory: -4.4MiB live, 73.1MiB allocated
Compiler: Compiled 4 805 to 574 computations (88.1% saved)

prune25.0ms (1.2%)

Memory

11.6MiB live, 49.1MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	503	3	506
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	504	7	511

Accuracy

100.0%

Counts

511 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	17.4%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
▶	3.0%	(sqrt.f64 (+.f64 x x))
✓	48.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	55.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 46 to 37 computations (19.6% saved)

simplify5.0ms (0.3%)

Memory

6.2MiB live, 6.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 6 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
cost-diff	0	(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))
cost-diff	0	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
cost-diff	-128	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
cost-diff	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	93
0	32	85
1	52	70
2	101	70
3	142	70
4	144	70
0	144	67

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 1/2 binary64)
x
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
(.f64 (.f64 x x) (*.f64 x x))
(*.f64 x x)

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

localize63.0ms (3%)

Memory

6.6MiB live, 88.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
accuracy	0.0546875	(.f64 (.f64 x x) (*.f64 x x))
accuracy	16.006120190797283	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
accuracy	22.98196929739655	(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.21484375	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	0.45703125	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

27.0ms	117×	0	valid
23.0ms	139×	0	invalid

Compiler

Compiled 172 to 38 computations (77.9% saved)

Precisions

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

ival-exp: 9.0ms (23.1% of total)

ival-mult: 8.0ms (20.6% of total)

ival-pow2: 6.0ms (15.4% of total)

ival-sqrt: 5.0ms (12.9% of total)

ival-pow: 4.0ms (10.3% of total)

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

ival-add: 2.0ms (5.1% of total)

ival-div: 1.0ms (2.6% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.7%)

Memory

-19.6MiB live, 17.9MiB allocated

Counts

12 → 108

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 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)) #<representation binary64>) () ())
#s(alt (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) (patch (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x) #<representation binary64>) () ())
#s(alt (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (patch (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))) (patch (sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))) (patch (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 6 binary64)) (patch (pow.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 #s(literal 2 binary64)) (patch (log.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) (.f64 x x)) (patch (.f64 (.f64 x x) (.f64 x x)) #<representation binary64>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

((exp (* (log 2) 1/2)) (sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (sqrt (+ x x)) (+ x x) (sqrt (/ (* 2 (pow x 6)) (* (* x x) (* x x)))) (/ (* 2 (pow x 6)) (* (* x x) (* x x))) (* 2 (pow x 6)) (pow x 6) (log 2) (* (* x x) (* x x)))

2.0ms

-inf

((exp (* (log 2) 1/2)) (sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (sqrt (+ x x)) (+ x x) (sqrt (/ (* 2 (pow x 6)) (* (* x x) (* x x)))) (/ (* 2 (pow x 6)) (* (* x x) (* x x))) (* 2 (pow x 6)) (pow x 6) (log 2) (* (* x x) (* x x)))

2.0ms

inf

((exp (* (log 2) 1/2)) (sqrt (+ (pow x 2) (pow x 2))) (* (exp (* (log 2) 1/2)) x) (* (log 2) 1/2) (sqrt (+ x x)) (+ x x) (sqrt (/ (* 2 (pow x 6)) (* (* x x) (* x x)))) (/ (* 2 (pow x 6)) (* (* x x) (* x x))) (* 2 (pow x 6)) (pow x 6) (log 2) (* (* x x) (* x x)))

simplify11.0ms (0.5%)

Memory

17.2MiB live, 17.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	456
1	40	456
2	86	456
3	143	456
4	160	456
5	206	456
6	251	456
7	282	456
8	343	456
9	357	456
10	357	456
0	357	456

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

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

rewrite55.0ms (2.6%)

Memory

-17.5MiB live, 58.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	83
0	32	69
1	91	58
0	525	56

Stop Event

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

Counts

12 → 147

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 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x)))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
(log.f64 #s(literal 2 binary64))
(.f64 (.f64 x x) (*.f64 x x))

Outputs
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eval27.0ms (1.3%)

Memory: 3.3MiB live, 47.2MiB allocated
Compiler: Compiled 2 654 to 439 computations (83.5% saved)

prune15.0ms (0.7%)

Memory

-6.7MiB live, 31.6MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	254	8	262

Accuracy

100.0%

Counts

262 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	43.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
✓	17.4%	(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
✓	3.0%	(sqrt.f64 (+.f64 x x))
✓	48.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	55.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 56 to 43 computations (23.2% saved)

simplify3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 2 binary64) (*.f64 x x))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)))
cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	26
0	10	26
1	15	26
2	18	26
0	18	26

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x

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

localize19.0ms (0.9%)

Memory

24.9MiB live, 24.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.4267997240306267	(/.f64 #s(literal 2 binary64) (*.f64 x x))
accuracy	33.120962586579886	(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)))
accuracy	33.365477848418784	(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))

Samples

13.0ms

256×

valid

Compiler

Compiled 54 to 14 computations (74.1% saved)

Precisions

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

ival-mult: 3.0ms (41.6% of total)

ival-div: 2.0ms (27.7% of total)

ival-sqrt: 2.0ms (27.7% of total)

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

exact: 0.0ms (0% of total)

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

series43.0ms (2%)

Memory

-31.9MiB live, 7.3MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

40.0ms

inf

((* (sqrt (/ 2 (* x x))) (* x x)) (sqrt (/ 2 (* x x))) (/ 2 (* x x)) (* x x))

1.0ms

-inf

((* (sqrt (/ 2 (* x x))) (* x x)) (sqrt (/ 2 (* x x))) (/ 2 (* x x)) (* x x))

1.0ms

((* (sqrt (/ 2 (* x x))) (* x x)) (sqrt (/ 2 (* x x))) (/ 2 (* x x)) (* x x))

simplify6.0ms (0.3%)

Memory

6.9MiB live, 6.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	200
1	20	200
2	36	200
3	45	200
4	53	200
5	68	200
6	83	200
7	99	200
8	119	200
9	124	200
10	125	200
0	125	200

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

rewrite182.0ms (8.6%)

Memory

-23.8MiB live, 109.4MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	30	22
2	123	20
3	622	16
4	4976	16
0	9741	16

Stop Event

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

Counts

4 → 505

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (*.f64 x x)))
(/.f64 #s(literal 2 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
#<batchref>
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eval59.0ms (2.8%)

Memory: 47.0MiB live, 113.6MiB allocated
Compiler: Compiled 8 718 to 1 762 computations (79.8% saved)

prune32.0ms (1.5%)

Memory

-21.8MiB live, 64.6MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	665	2	667
Fresh	0	0	0
Picked	0	1	1
Done	2	5	7
Total	667	8	675

Accuracy

100.0%

Counts

675 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	46.6%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	55.1%	(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) x))
✓	43.6%	(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
✓	3.0%	(sqrt.f64 (+.f64 x x))
✓	48.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	46.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	55.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 132 to 82 computations (37.9% saved)

regimes49.0ms (2.3%)

Memory

-9.5MiB live, 29.0MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
(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)))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))
(hypot.f64 x x)
(/.f64 #s(literal -1 binary64) (/.f64 (pow.f64 #s(literal 4 binary64) #s(literal -1/4 binary64)) x))
(sqrt.f64 (/.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (.f64 (.f64 x x) (.f64 x x))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))

Outputs
(hypot.f64 x x)

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	x
4.0ms	(pow.f64 x #s(literal 2 binary64))
4.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes11.0ms (0.5%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
(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)))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (.f64 x x))) (*.f64 x x))

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

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

Results

Accuracy	Segments	Branch
99.4%	2	`x`
75.0%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
75.0%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
75.0%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes3.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(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

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes7.0ms (0.3%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(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:

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

Results

Accuracy	Segments	Branch
46.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
46.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
46.5%	1	`(pow.f64 x #s(literal 2 binary64))`
46.5%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes18.0ms (0.9%)

Memory

-27.1MiB live, 11.9MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	x
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
3.0%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.0%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.0%	1	`(pow.f64 x #s(literal 2 binary64))`
3.0%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch14.0ms (0.7%)

Memory

17.7MiB live, 17.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.5832068541930837e-296	8.216140364027227e-308

Samples

7.0ms

160×

valid

Compiler

Compiled 111 to 128 computations (-15.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (53.7% of total)

ival-add: 1.0ms (26.9% of total)

ival-sqrt: 1.0ms (26.9% of total)

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

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

bsearch1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.5832068541930837e-296	8.216140364027227e-308

Compiler

Compiled 121 to 138 computations (-14% saved)

simplify31.0ms (1.4%)

Memory

-8.9MiB live, 35.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	73
1	29	73
2	36	73
3	41	73
4	44	73
5	45	73

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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))
(sqrt.f64 (+.f64 x x))

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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 -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 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))
(sqrt.f64 (+.f64 x x))

soundness372.0ms (17.5%)

Memory

-6.4MiB live, 316.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	30	22
2	123	20
3	622	16
4	4976	16
0	9741	16
0	5	18
0	8	14
1	28	10
0	170	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	20	83
0	32	69
1	91	58
0	525	56
0	24	90
0	40	56
1	122	56
0	707	56

Stop Event

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

Compiler

Compiled 178 to 104 computations (41.6% saved)

preprocess77.0ms (3.6%)

Memory: -11.8MiB live, 64.2MiB allocated
Compiler: Compiled 98 to 46 computations (53.1% 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	24	109
0	40	90
1	56	90
2	72	90
3	83	90
4	89	90
5	100	90
6	128	90
7	147	90
8	162	90
9	241	90
10	380	90
11	395	90
12	400	90
0	400	90

Iter	Nodes	Cost
0	15	644
1	25	644
2	39	644
3	43	644
4	51	644
5	62	644
6	73	644
7	95	644
8	106	644
9	106	644
0	106	644

Iter	Nodes	Cost
0	22	456
1	40	456
2	86	456
3	143	456
4	160	456
5	206	456
6	251	456
7	282	456
8	343	456
9	357	456
10	357	456
0	357	456

Iter	Nodes	Cost
0	10	200
1	20	200
2	36	200
3	45	200
4	53	200
5	68	200
6	83	200
7	99	200
8	119	200
9	124	200
10	125	200
0	125	200

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	24	109
0	40	90
1	56	90
2	72	90
3	83	90
4	89	90
5	100	90
6	128	90
7	147	90
8	162	90
9	241	90
10	380	90
11	395	90
12	400	90
0	400	90

Iter	Nodes	Cost
0	15	644
1	25	644
2	39	644
3	43	644
4	51	644
5	62	644
6	73	644
7	95	644
8	106	644
9	106	644
0	106	644

Iter	Nodes	Cost
0	22	456
1	40	456
2	86	456
3	143	456
4	160	456
5	206	456
6	251	456
7	282	456
8	343	456
9	357	456
10	357	456
0	357	456

Iter	Nodes	Cost
0	10	200
1	20	200
2	36	200
3	45	200
4	53	200
5	68	200
6	83	200
7	99	200
8	119	200
9	124	200
10	125	200
0	125	200

start0.0ms (0%)

analyze0.0ms (0%)

sample587.0ms (27.7%)

explain74.0ms (3.5%)

preprocess16.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize21.0ms (1%)

series4.0ms (0.2%)

simplify5.0ms (0.2%)

rewrite33.0ms (1.6%)

eval8.0ms (0.4%)

prune10.0ms (0.5%)

simplify13.0ms (0.6%)

localize94.0ms (4.4%)

series12.0ms (0.6%)

simplify7.0ms (0.3%)

rewrite44.0ms (2.1%)

eval47.0ms (2.2%)

prune25.0ms (1.2%)

simplify5.0ms (0.3%)

localize63.0ms (3%)

series16.0ms (0.7%)

simplify11.0ms (0.5%)

rewrite55.0ms (2.6%)

eval27.0ms (1.3%)

prune15.0ms (0.7%)

simplify3.0ms (0.1%)

localize19.0ms (0.9%)

series43.0ms (2%)

simplify6.0ms (0.3%)

rewrite182.0ms (8.6%)

eval59.0ms (2.8%)

prune32.0ms (1.5%)

regimes49.0ms (2.3%)

regimes11.0ms (0.5%)

regimes3.0ms (0.1%)

regimes7.0ms (0.3%)

regimes18.0ms (0.9%)

bsearch14.0ms (0.7%)

bsearch1.0ms (0.1%)

simplify31.0ms (1.4%)

soundness372.0ms (17.5%)

preprocess77.0ms (3.6%)

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	24	109
0	40	90
1	56	90
2	72	90
3	83	90
4	89	90
5	100	90
6	128	90
7	147	90
8	162	90
9	241	90
10	380	90
11	395	90
12	400	90
0	400	90

Iter	Nodes	Cost
0	15	644
1	25	644
2	39	644
3	43	644
4	51	644
5	62	644
6	73	644
7	95	644
8	106	644
9	106	644
0	106	644

Iter	Nodes	Cost
0	22	456
1	40	456
2	86	456
3	143	456
4	160	456
5	206	456
6	251	456
7	282	456
8	343	456
9	357	456
10	357	456
0	357	456

Iter	Nodes	Cost
0	10	200
1	20	200
2	36	200
3	45	200
4	53	200
5	68	200
6	83	200
7	99	200
8	119	200
9	124	200
10	125	200
0	125	200