Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample634.0ms (43.5%)

Memory

-17.1MiB live, 510.8MiB allocated

Samples

486.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 300.0ms

ival-hypot: 292.0ms (97.3% of total)

ival-true: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

explain63.0ms (4.3%)

Memory

-16.2MiB live, 109.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
128	-	1	(-8.760384076060712e-156)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	65	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	65
↳	`(*.f64 x x)`	overflow	130
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	62	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	62
↳	`(*.f64 x x)`	underflow	124

Confusion

	Predicted +	Predicted -
+	127	1
-	0	128

Precision

1.0

Recall

0.9921875

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	127	0	1
-	0	0	128

Precision?

1.0

Recall?

0.9921875

Freqs

test

number	freq
0	129
1	127

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

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

ival-hypot: 8.0ms (56.5% of total)

ival-mult: 3.0ms (21.2% of total)

ival-add: 2.0ms (14.1% of total)

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

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

preprocess16.0ms (1.1%)

Memory

32.1MiB live, 32.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 4 computations (50% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.8%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 8 to 4 computations (50% saved)

simplify5.0ms (0.4%)

Memory

-31.4MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-5184	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
cost-diff	0	(*.f64 x x)
cost-diff	192	(+.f64 (.f64 x x) (.f64 x x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
1	11	15
2	14	15
3	17	15
0	17	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (1.2%)

Memory

-1.1MiB live, 40.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (.f64 x x) (.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	29.55904743934345	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

11.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

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

ival-hypot: 4.0ms (59.9% of total)

ival-add: 1.0ms (15% of total)

ival-mult: 1.0ms (15% of total)

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

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

series4.0ms (0.3%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

#s(alt (+.f64 (*.f64 x x) (*.f64 x x)) (patch (+.f64 (*.f64 x x) (*.f64 x x)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

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

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

Calls

3 calls:

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

simplify5.0ms (0.4%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite34.0ms (2.3%)

Memory

-5.3MiB live, 71.0MiB allocated

Rules

66×	`lower-*.f32`
64×	`lower-*.f64`
42×	`lower-fma.f64`
42×	`lower-fma.f32`
34×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

eval8.0ms (0.5%)

Memory: 25.1MiB live, 25.1MiB allocated
Compiler: Compiled 669 to 107 computations (84% saved)

prune6.0ms (0.4%)

Memory

-26.1MiB live, 11.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Accuracy

100.0%

Counts

86 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(hypot.f64 x x)
▶	99.4%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
▶	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify4.0ms (0.3%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	54
0	25	51
1	33	51
2	34	51
0	34	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize45.0ms (3.1%)

Memory

-20.4MiB live, 64.3MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0390625	(hypot.f64 x x)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
accuracy	0	(sqrt.f64 x)
accuracy	0.37337875976844204	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
accuracy	0	(.f64 (.f64 x x) #s(literal 2 binary64))
accuracy	0	(*.f64 x x)
accuracy	29.55904743934345	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
accuracy	0.41796875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

27.0ms

256×

valid

Compiler

Compiled 61 to 14 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 7.0ms (38.5% of total)

ival-sqrt: 7.0ms (38.5% of total)

ival-hypot: 4.0ms (22% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.6%)

Memory

22.3MiB live, 22.3MiB allocated

Counts

11 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

1.0ms

inf

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

1.0ms

((sqrt (+ (* x x) (* x x))) (* (sqrt 2) x) (sqrt 2) (* (* x x) 2) (* x x) (sqrt (* (* x x) 2)) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x) (sqrt (+ (* x x) (* x x))))

simplify133.0ms (9.1%)

Memory

-12.7MiB live, 63.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 460×	`associate-r`
1 232×	`lower-*.f64`
1 232×	`lower-fma.f64`
1 232×	`lower-fma.f32`
1 232×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	500
1	50	500
2	136	500
3	263	500
4	491	500
5	809	500
6	1420	500
7	1546	500
8	1601	500
9	1639	500
10	1822	500
11	2036	500
12	2080	500
13	2108	500
14	2112	500
15	2112	500
16	2253	500
17	2437	500
18	3518	500
19	3636	500
20	3660	500
21	3668	500
22	3672	500
23	3676	500
24	3788	500
25	3836	500
26	3836	500
27	4001	500
0	4001	500

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 120

Calls

Call 1

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

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

rewrite34.0ms (2.3%)

Memory

24.7MiB live, 67.8MiB allocated

Rules

90×	`lower-*.f32`
80×	`lower-*.f64`
42×	`lower-fma.f64`
42×	`lower-fma.f32`
38×	`lower-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
0	25	40
1	53	38
0	203	38

Stop Event

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

Counts

11 → 83

Calls

Call 1

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

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

eval18.0ms (1.3%)

Memory: 2.4MiB live, 41.6MiB allocated
Compiler: Compiled 1 419 to 169 computations (88.1% saved)

prune76.0ms (5.2%)

Memory

-11.9MiB live, 26.2MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	202	5	207

Accuracy

100.0%

Counts

207 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify4.0ms (0.3%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
cost-diff	0	(*.f64 (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 (+ (* x x) (* x x))) (.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)))

Rules

26×	`lower-*.f32`
20×	`lower-*.f64`
10×	`*-commutative`
8×	`lower-sqrt.f32`
6×	`lift-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
0	23	46
1	32	43
2	40	43
0	40	40

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize41.0ms (2.8%)

Memory

-20.6MiB live, 58.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.37337875976844204	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))
accuracy	0.41796875	(.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x)
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

29.0ms

256×

valid

Compiler

Compiled 48 to 14 computations (70.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-hypot: 5.0ms (26.5% of total)

ival-mult: 4.0ms (21.2% of total)

ival-log: 3.0ms (15.9% of total)

ival-sqrt: 3.0ms (15.9% of total)

ival-exp: 2.0ms (10.6% of total)

ival-add: 1.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.3%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

9 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify86.0ms (5.9%)

Memory

-0.2MiB live, 38.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 078×	`associate-r`
944×	`lower-*.f64`
944×	`lower-fma.f64`
944×	`lower-fma.f32`
944×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	300
1	46	300
2	130	300
3	257	300
4	492	300
5	806	300
6	1407	300
7	1535	300
8	1587	300
9	1611	300
10	1730	300
11	1921	300
12	1961	300
13	1989	300
14	1993	300
15	1993	300
16	2177	300
17	2281	300
18	2883	300
19	3229	300
20	3241	300
0	3241	300

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

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

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

rewrite32.0ms (2.2%)

Memory

-3.7MiB live, 35.0MiB allocated

Rules

96×	`lower-*.f32`
90×	`lower-*.f64`
68×	`lower-fma.f64`
68×	`lower-fma.f32`
54×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	23	43
1	52	34
0	261	31

Stop Event

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

Counts

9 → 71

Calls

Call 1

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

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

eval16.0ms (1.1%)

Memory: -6.0MiB live, 30.8MiB allocated
Compiler: Compiled 1 198 to 200 computations (83.3% saved)

prune8.0ms (0.6%)

Memory

20.8MiB live, 20.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	143	5	148

Accuracy

100.0%

Counts

148 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	53.8%	(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) x))

Compiler

Compiled 73 to 49 computations (32.9% saved)

regimes18.0ms (1.2%)

Memory

-22.1MiB live, 20.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

10.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.9%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.9%	1	`(*.f64 x x)`

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes9.0ms (0.6%)

Memory

17.7MiB live, 17.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

regimes7.0ms (0.5%)

Memory

16.8MiB live, 16.8MiB allocated

Accuracy

Total -29.3b remaining (-7016%)

Threshold costs -29.3b (-7016%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 19 to 10 computations (47.4% saved)

simplify26.0ms (1.8%)

Memory

-28.0MiB live, 45.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	15	23

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness68.0ms (4.7%)

Memory

-3.8MiB live, 77.6MiB allocated

Rules

90×	`lower-*.f32`
80×	`lower-*.f64`
66×	`lower-*.f32`
64×	`lower-*.f64`
42×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	16	47
0	25	40
1	53	38
0	203	38

Stop Event

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

Compiler

Compiled 59 to 37 computations (37.3% saved)

preprocess25.0ms (1.8%)

Memory: 12.6MiB live, 49.9MiB allocated
Remove: (abs x)
Compiler: Compiled 58 to 36 computations (37.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

Iter	Nodes	Cost
0	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	4	18
0	7	14
1	23	10
0	160	9
0	16	47
0	25	40
1	53	38
0	203	38

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

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

Iter	Nodes	Cost
0	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	4	18
0	7	14
1	23	10
0	160	9
0	16	47
0	25	40
1	53	38
0	203	38

start0.0ms (0%)

analyze0.0ms (0%)

sample634.0ms (43.5%)

explain63.0ms (4.3%)

preprocess16.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.4%)

localize18.0ms (1.2%)

series4.0ms (0.3%)

simplify5.0ms (0.4%)

rewrite34.0ms (2.3%)

eval8.0ms (0.5%)

prune6.0ms (0.4%)

simplify4.0ms (0.3%)

localize45.0ms (3.1%)

series8.0ms (0.6%)

simplify133.0ms (9.1%)

rewrite34.0ms (2.3%)

eval18.0ms (1.3%)

prune76.0ms (5.2%)

simplify4.0ms (0.3%)

localize41.0ms (2.8%)

series5.0ms (0.3%)

simplify86.0ms (5.9%)

rewrite32.0ms (2.2%)

eval16.0ms (1.1%)

prune8.0ms (0.6%)

regimes18.0ms (1.2%)

regimes9.0ms (0.6%)

regimes7.0ms (0.5%)

simplify26.0ms (1.8%)

soundness68.0ms (4.7%)

preprocess25.0ms (1.8%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	4	18
0	7	14
1	23	10
0	160	9
0	16	47
0	25	40
1	53	38
0	203	38