Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample1.1s (42%)

Memory

0.0MiB live, 731.4MiB allocated

Samples

885.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 218.0ms

ival-hypot: 210.0ms (96.3% of total)

ival-true: 5.0ms (2.3% of total)

ival-assert: 4.0ms (1.8% of total)

Bogosity

explain103.0ms (4%)

Memory

-4.7MiB live, 73.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	6	(1.1409386054263518e-160)	`(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	60	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	60
↳	`(*.f64 x x)`	overflow	120
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	59	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	59
↳	`(*.f64 x x)`	underflow	118

Confusion

	Predicted +	Predicted -
+	119	6
-	0	131

Precision

1.0

Recall

0.952

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	119	0	6
-	0	0	131

Precision?

1.0

Recall?

0.952

Freqs

test

number	freq
0	137
1	119

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

61.0ms

512×

valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-add: 39.0ms (76.4% of total)

ival-hypot: 8.0ms (15.7% of total)

ival-mult: 3.0ms (5.9% of total)

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

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

preprocess16.0ms (0.6%)

Memory

21.3MiB live, 21.3MiB 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)))
(sqrt.f64 (*.f64 x (+.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

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

prune20.0ms (0.8%)

Memory

-36.3MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.7%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
cost-diff	320	(+.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)))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
(*.f64 x x)
x

localize17.0ms (0.7%)

Memory

25.4MiB live, 25.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(+.f64 (.f64 x x) (.f64 x x))
accuracy	28.35311497398119	(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 (59.3% of total)

ival-mult: 2.0ms (29.6% of total)

ival-add: 1.0ms (14.8% of total)

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

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

series3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB 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 (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) (patch (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.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 (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) (patch (sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x))) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.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 (* 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 (* 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 (* 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 (* 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 (* -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>) () ())) ())
#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 (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 (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

9 calls:

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

simplify13.0ms (0.5%)

Memory

-29.4MiB live, 6.1MiB 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))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite31.0ms (1.2%)

Memory

34.9MiB live, 34.9MiB 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))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 x x)

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

eval33.0ms (1.3%)

Memory: -51.8MiB live, 10.2MiB allocated
Compiler: Compiled 750 to 94 computations (87.5% saved)

prune7.0ms (0.3%)

Memory

8.9MiB live, 8.9MiB 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
▶	100.0%	(hypot.f64 x x)
▶	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	55.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 25 to 15 computations (40% saved)

simplify5.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	5312	(hypot.f64 x x)
cost-diff	0	(+.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 x x)
cost-diff	0	(*.f64 (+.f64 x x) x)
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x x) x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	52
0	23	49
1	28	49
2	31	49
0	31	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize39.0ms (1.5%)

Memory

-11.6MiB live, 65.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(hypot.f64 x x)
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.35384750976844204	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	28.35311497398119	(sqrt.f64 (*.f64 (+.f64 x x) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.44921875	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))

Samples

25.0ms

256×

valid

Compiler

Compiled 59 to 13 computations (78% saved)

Precisions

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

ival-sqrt: 6.0ms (36.4% of total)

ival-mult: 5.0ms (30.3% of total)

ival-hypot: 4.0ms (24.2% of total)

ival-add: 1.0ms (6.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

10 → 108

Calls

Call 1

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

Calls

27 calls:

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

simplify142.0ms (5.5%)

Memory

-10.3MiB live, 69.1MiB allocated

Algorithm

1×	egg-herbie

Rules

1 478×	`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	464
1	50	464
2	136	464
3	265	464
4	490	464
5	809	464
6	1411	464
7	1537	464
8	1592	464
9	1630	464
10	1808	464
11	2022	464
12	2068	464
13	2096	464
14	2100	464
15	2100	464
16	2246	464
17	2430	464
18	3585	464
19	3703	464
20	3727	464
21	3735	464
22	3739	464
23	3743	464
24	3855	464
25	3903	464
26	3903	464
27	4085	464
0	4085	464

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

rewrite32.0ms (1.3%)

Memory

3.2MiB live, 42.2MiB allocated

Rules

98×	`lower-*.f32`
92×	`lower-*.f64`
68×	`lower-fma.f64`
68×	`lower-fma.f32`
58×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	44
0	23	38
1	51	34
0	255	34

Stop Event

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

Counts

10 → 127

Calls

Call 1

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

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

eval24.0ms (0.9%)

Memory: 7.4MiB live, 45.4MiB allocated
Compiler: Compiled 2 492 to 231 computations (90.7% saved)

prune21.0ms (0.8%)

Memory

2.0MiB live, 41.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	270	3	273
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	270	7	277

Accuracy

100.0%

Counts

277 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	7.1%	(sqrt.f64 (+.f64 x x))
▶	21.2%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
✓	55.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 66 to 37 computations (43.9% saved)

simplify188.0ms (7.3%)

Memory

13.3MiB live, 286.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 x x))
cost-diff	0	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
cost-diff	64	(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
cost-diff	1216	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x))))
cost-diff	2432	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))
cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

7 530×	`lower-fma.f32`
7 528×	`lower-fma.f64`
6 908×	`lower-*.f32`
6 896×	`lower-*.f64`
1 970×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	174
0	38	148
1	66	79
2	195	71
3	1310	71
4	3521	71
5	5052	71
6	6564	71
7	7926	71
0	8051	65

Stop Event

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

Calls

Call 1

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

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

localize67.0ms (2.6%)

Memory

-3.2MiB live, 84.0MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x))))
accuracy	28.35311497398119	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))) x))
accuracy	48.65235395301359	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 0 binary64)) (+.f64 x x)))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
accuracy	0.44921875	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
accuracy	1.0	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

46.0ms

256×

valid

Compiler

Compiled 178 to 23 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 9.0ms (30% of total)

ival-log: 5.0ms (16.7% of total)

ival-hypot: 4.0ms (13.3% of total)

ival-div: 3.0ms (10% of total)

ival-sqrt: 3.0ms (10% of total)

ival-add: 2.0ms (6.7% of total)

ival-exp: 2.0ms (6.7% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

12 → 108

Calls

Call 1

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

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

Calls

27 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x)))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(/ 1 (/ (+ (* x (* x (* x x))) 0) (* (+ (* x (* x (* x x))) 0) (+ x x))))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	0	(+ (* x (* x (* x x))) 0)

simplify19.0ms (0.7%)

Memory

-23.2MiB live, 12.8MiB allocated

Algorithm

1×	egg-herbie

Rules

138×	`lower-*.f64`
138×	`lower-fma.f64`
138×	`lower-fma.f32`
138×	`lower-*.f32`
96×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	408
1	39	408
2	83	408
3	140	408
4	156	408
5	202	408
6	247	408
7	278	408
8	339	408
9	353	408
10	353	408
0	353	408

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

rewrite50.0ms (1.9%)

Memory

17.9MiB live, 54.4MiB allocated

Rules

174×	`lower-*.f32`
166×	`lower-*.f64`
148×	`lower-/.f64`
148×	`lower-/.f32`
146×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	124
0	38	64
1	118	29
0	1044	29

Stop Event

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

Counts

12 → 45

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

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

eval21.0ms (0.8%)

Memory: 3.0MiB live, 40.2MiB allocated
Compiler: Compiled 4 273 to 359 computations (91.6% saved)

prune34.0ms (1.3%)

Memory

-6.0MiB live, 38.3MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	218	8	226

Accuracy

100.0%

Counts

226 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.1%	(sqrt.f64 (+.f64 x x))
▶	21.2%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
✓	55.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 67 to 40 computations (40.3% saved)

simplify226.0ms (8.8%)

Memory

10.3MiB live, 234.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
cost-diff	64	(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
cost-diff	1216	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))))
cost-diff	2432	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))

Rules

7 760×	`lower-fma.f32`
7 758×	`lower-fma.f64`
6 470×	`lower-*.f32`
6 460×	`lower-*.f64`
1 884×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	132
0	24	117
1	50	47
2	188	41
3	1156	41
4	3343	41
5	4929	41
6	6523	41
7	6926	41
8	7029	41
9	7126	41
10	7366	41
11	7470	41
0	8092	38

Stop Event

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

Calls

Call 1

Inputs
#s(literal 0 binary64)
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))))
#s(literal 1 binary64)
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
x
(.f64 x (.f64 x x))
(*.f64 x x)
#s(literal 0 binary64)
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))
(.f64 (.f64 x (*.f64 x x)) x)
(+.f64 x x)

Outputs
#s(literal 0 binary64)
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x)
(*.f64 x (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))))
(+.f64 x x)
#s(literal 1 binary64)
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))
(/.f64 #s(literal 1/2 binary64) x)
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(.f64 x (.f64 x (*.f64 x x)))
x
(.f64 x (.f64 x x))
(*.f64 x x)
#s(literal 0 binary64)
(.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))
(.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 x x)))
(.f64 (.f64 x (*.f64 x x)) x)
(.f64 x (.f64 x (*.f64 x x)))
(+.f64 x x)

localize43.0ms (1.7%)

Memory

-15.1MiB live, 72.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))))
accuracy	28.35311497398119	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
accuracy	48.65235395301359	(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))

Samples

25.0ms

256×

valid

Compiler

Compiled 139 to 16 computations (88.5% saved)

Precisions

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

ival-mult: 8.0ms (47.8% of total)

ival-div: 4.0ms (23.9% of total)

ival-add: 2.0ms (11.9% of total)

ival-sqrt: 2.0ms (11.9% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))) (patch (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))) #<representation binary64>) () ())
#s(alt (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (patch (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))) x)) (patch (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))) x)) #<representation binary64>) () ())
#s(alt (.f64 x (.f64 x x)) (patch (.f64 x (.f64 x x)) #<representation binary64>) () ())

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

Calls

15 calls:

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

simplify7.0ms (0.3%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	196
1	22	196
2	35	196
3	39	196
4	43	196
5	55	196
6	67	196
7	78	196
8	98	196
9	103	196
0	103	196

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

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

rewrite42.0ms (1.6%)

Memory

8.4MiB live, 46.1MiB allocated

Rules

166×	`lower-*.f32`
160×	`lower-*.f64`
148×	`lower-/.f64`
148×	`lower-/.f32`
96×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	80
0	24	53
1	95	9
0	891	9

Stop Event

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

Counts

5 → 31

Calls

Call 1

Inputs
(/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x))))
(fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (*.f64 x x)) x) (+.f64 x x)))) x))
(.f64 x (.f64 x x))

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

eval22.0ms (0.9%)

Memory: -22.4MiB live, 14.6MiB allocated
Compiler: Compiled 2 260 to 205 computations (90.9% saved)

prune10.0ms (0.4%)

Memory

14.6MiB live, 14.6MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	0	0
Picked	1	1	2
Done	0	6	6
Total	108	8	116

Accuracy

100.0%

Counts

116 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.4%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	7.1%	(sqrt.f64 (+.f64 x x))
	21.2%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (+.f64 x x)))) x))
✓	55.7%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.1%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 184 to 76 computations (58.7% saved)

regimes15.0ms (0.6%)

Memory

16.8MiB live, 16.8MiB allocated

Counts

11 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

4.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(+.f64 (.f64 x x) (.f64 x x))
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes20.0ms (0.8%)

Memory

-19.7MiB live, 19.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

9.0ms	(*.f64 x x)
4.0ms	x
3.0ms	(+.f64 (.f64 x x) (.f64 x x))
3.0ms	(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 23 to 10 computations (56.5% saved)

regimes9.0ms (0.3%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(*.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 23 to 10 computations (56.5% saved)

regimes23.0ms (0.9%)

Memory

-26.6MiB live, 22.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

18.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	x
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
7.1%	1	`x`
7.1%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
7.1%	1	`(+.f64 (.f64 x x) (.f64 x x))`
7.1%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.2%)

Memory

11.3MiB live, 11.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
3.8%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.8%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.8%	1	`(*.f64 x x)`
3.8%	1	`x`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	16	28

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

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

soundness131.0ms (5.1%)

Memory

-17.0MiB live, 138.3MiB allocated

Rules

174×	`lower-*.f32`
166×	`lower-*.f64`
148×	`lower-/.f64`
148×	`lower-/.f32`
146×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	44
0	23	38
1	51	34
0	255	34
0	23	124
0	38	64
1	118	29
0	1044	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 102 to 50 computations (51% saved)

preprocess31.0ms (1.2%)

Memory: -10.2MiB live, 65.1MiB allocated
Remove: (abs x)
Compiler: Compiled 68 to 32 computations (52.9% 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	21	408
1	39	408
2	83	408
3	140	408
4	156	408
5	202	408
6	247	408
7	278	408
8	339	408
9	353	408
10	353	408
0	353	408

Iter	Nodes	Cost
0	13	196
1	22	196
2	35	196
3	39	196
4	43	196
5	55	196
6	67	196
7	78	196
8	98	196
9	103	196
0	103	196

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	21	408
1	39	408
2	83	408
3	140	408
4	156	408
5	202	408
6	247	408
7	278	408
8	339	408
9	353	408
10	353	408
0	353	408

Iter	Nodes	Cost
0	13	196
1	22	196
2	35	196
3	39	196
4	43	196
5	55	196
6	67	196
7	78	196
8	98	196
9	103	196
0	103	196

start0.0ms (0%)

analyze0.0ms (0%)

sample1.1s (42%)

explain103.0ms (4%)

preprocess16.0ms (0.6%)

eval0.0ms (0%)

prune20.0ms (0.8%)

simplify4.0ms (0.2%)

localize17.0ms (0.7%)

series3.0ms (0.1%)

simplify13.0ms (0.5%)

rewrite31.0ms (1.2%)

eval33.0ms (1.3%)

prune7.0ms (0.3%)

simplify5.0ms (0.2%)

localize39.0ms (1.5%)

series6.0ms (0.2%)

simplify142.0ms (5.5%)

rewrite32.0ms (1.3%)

eval24.0ms (0.9%)

prune21.0ms (0.8%)

simplify188.0ms (7.3%)

localize67.0ms (2.6%)

series6.0ms (0.2%)

simplify19.0ms (0.7%)

rewrite50.0ms (1.9%)

eval21.0ms (0.8%)

prune34.0ms (1.3%)

simplify226.0ms (8.8%)

localize43.0ms (1.7%)

series2.0ms (0.1%)

simplify7.0ms (0.3%)

rewrite42.0ms (1.6%)

eval22.0ms (0.9%)

prune10.0ms (0.4%)

regimes15.0ms (0.6%)

regimes20.0ms (0.8%)

regimes9.0ms (0.3%)

regimes23.0ms (0.9%)

regimes5.0ms (0.2%)

simplify5.0ms (0.2%)

soundness131.0ms (5.1%)

preprocess31.0ms (1.2%)

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	21	408
1	39	408
2	83	408
3	140	408
4	156	408
5	202	408
6	247	408
7	278	408
8	339	408
9	353	408
10	353	408
0	353	408

Iter	Nodes	Cost
0	13	196
1	22	196
2	35	196
3	39	196
4	43	196
5	55	196
6	67	196
7	78	196
8	98	196
9	103	196
0	103	196