Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample535.0ms (14%)

Memory

-7.6MiB live, 1 030.7MiB allocated

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-hypot: 203.0ms (95.8% of total)

ival-true: 6.0ms (2.8% of total)

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

Bogosity

explain81.0ms (2.1%)

Memory

15.3MiB live, 92.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
128	-	-	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	-	`(*.f64 x x)`
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	77	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	77
↳	`(*.f64 x x)`	overflow	154
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	51	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	51
↳	`(*.f64 x x)`	underflow	102

Confusion

	Predicted +	Predicted -
+	128	1
-	0	127

Precision

1.0

Recall

0.9922480620155039

Confusion?

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

Precision?

1.0

Recall?

0.9922480620155039

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms

512×

valid

Compiler

Compiled 51 to 16 computations (68.6% saved)

Precisions

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

ival-hypot: 11.0ms (63.6% of total)

ival-mult: 4.0ms (23.1% of total)

ival-add: 2.0ms (11.6% of total)

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

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

preprocess17.0ms (0.4%)

Memory

16.2MiB live, 16.2MiB 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.2%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB 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

localize67.0ms (1.7%)

Memory

-9.0MiB live, 29.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 x x))
accuracy	29.92347126976054	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

13.0ms

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 (54% of total)

ival-mult: 2.0ms (27% of total)

ival-add: 1.0ms (13.5% of total)

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

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

series3.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (+.f64 (.f64 x x) (.f64 x x))>
#<alt (sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))>
#<alt (*.f64 x x)>

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

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))

simplify12.0ms (0.3%)

Memory

-33.4MiB live, 8.1MiB 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)

rewrite34.0ms (0.9%)

Memory

15.6MiB live, 52.9MiB 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)))

eval8.0ms (0.2%)

Memory: 21.6MiB live, 21.6MiB allocated
Compiler: Compiled 750 to 94 computations (87.5% saved)

prune10.0ms (0.3%)

Memory

-14.1MiB live, 22.1MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Accuracy

100.0%

Counts

86 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	16.2%	(sqrt.f64 (/.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))))))
▶	53.2%	(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 104 to 52 computations (50% saved)

simplify501.0ms (13.1%)

Memory

5.8MiB live, 602.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.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))))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1216	(/.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)))))
cost-diff	2432	(/.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))))
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))))
cost-diff	5312	(hypot.f64 x x)

Rules

48 722×	`lower-fma.f32`
48 720×	`lower-fma.f64`
5 900×	`lower-*.f32`
5 888×	`lower-*.f64`
3 382×	`lower-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	162
0	41	112
1	61	92
2	213	86
3	1054	84
4	2970	84
5	3388	84
6	4016	84
7	5085	84
8	6020	84
9	6349	84
0	8427	84

Stop Event

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

Calls

Call 1

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

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

localize129.0ms (3.4%)

Memory

0.6MiB live, 165.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.11166000976844202	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	0.3152931330160837	(/.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)))))
accuracy	29.92347126976054	(sqrt.f64 (/.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))))))
accuracy	49.91115814046572	(/.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))))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.34765625	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	29.92347126976054	(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	0.42578125	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.01171875	(hypot.f64 x x)

Samples

106.0ms

256×

valid

Compiler

Compiled 177 to 23 computations (87% saved)

Precisions

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

ival-sqrt: 18.0ms (47.8% of total)

ival-mult: 10.0ms (26.5% of total)

ival-hypot: 5.0ms (13.3% of total)

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

ival-add: 2.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

12.1MiB live, 12.1MiB allocated

Counts

14 → 156

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>
#<alt #s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (*.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (sqrt.f64 (*.f64 (+.f64 x x) x))>
#<alt (*.f64 (+.f64 x x) x)>
#<alt (+.f64 x x)>
#<alt (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))>
#<alt (sqrt.f64 x)>
#<alt (sqrt.f64 (+.f64 x x))>
#<alt (/.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))))>
#<alt (/.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)))))>
#<alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))>
#<alt (sqrt.f64 (/.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))))))>

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>

Calls

39 calls:

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

simplify218.0ms (5.7%)

Memory

7.6MiB live, 150.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 808×	`lower-*.f64`
1 808×	`lower-*.f32`
1 680×	`lower-fma.f64`
1 680×	`lower-fma.f32`
1 116×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	672
1	54	672
2	142	672
3	266	672
4	497	672
5	813	672
6	1343	672
7	1469	672
8	1524	672
9	1576	672
10	1790	672
11	2032	672
12	2154	672
13	2270	672
14	2322	672
15	2348	672
16	2362	672
17	2364	672
18	2364	672
19	2532	672
20	3004	672
21	4858	672
22	5320	672
23	5443	672
24	5610	672
25	5724	672
26	5828	672
27	7210	672
28	7684	672
0	8126	672

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

rewrite69.0ms (1.8%)

Memory

1.2MiB live, 78.2MiB allocated

Rules

170×	`lower-*.f32`
166×	`lower-*.f64`
158×	`lower-/.f64`
158×	`lower-/.f32`
148×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	126
0	41	48
1	123	26
0	1078	26

Stop Event

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

Counts

14 → 47

Calls

Call 1

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

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

eval37.0ms (1%)

Memory: -6.0MiB live, 76.8MiB allocated
Compiler: Compiled 4 089 to 304 computations (92.6% saved)

prune14.0ms (0.4%)

Memory

1.6MiB live, 40.5MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	265	8	273

Accuracy

100.0%

Counts

273 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
▶	16.1%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))))
✓	53.2%	(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)))))
▶	3.6%	#s(literal 0 binary64)

Compiler

Compiled 72 to 43 computations (40.3% saved)

simplify720.0ms (18.8%)

Memory

-3.2MiB live, 786.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

60 494×	`lower-fma.f32`
60 492×	`lower-fma.f64`
6 130×	`lower-*.f32`
6 112×	`lower-*.f64`
3 578×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	190
0	49	159
1	81	113
2	229	107
3	1122	105
4	2929	105
5	3382	105
6	4013	105
7	5076	105
8	5997	105
9	6326	105
0	8525	99

Stop Event

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

Calls

Call 1

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

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

localize175.0ms (4.6%)

Memory

19.9MiB live, 192.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0	#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.34765625	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.448261279305326	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.11166000976844202	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	0.3152931330160837	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))))
accuracy	29.92347126976054	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))))
accuracy	49.91115814046572	(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.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	0.42578125	(.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

124.0ms

256×

valid

Compiler

Compiled 176 to 28 computations (84.1% saved)

Precisions

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

ival-mult: 14.0ms (37.2% of total)

ival-sqrt: 6.0ms (16% of total)

ival-hypot: 5.0ms (13.3% of total)

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

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

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

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

exact: 1.0ms (2.7% of total)

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

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

series4.0ms (0.1%)

Memory

-32.5MiB live, 5.6MiB allocated

Counts

14 → 120

Calls

Call 1

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

Outputs
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* x (* (sqrt -2) (sqrt -1))))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))>
#<alt (* -1 (* (sqrt x) (* (pow (sqrt -1) 2) (sqrt 2))))>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (sqrt x) (sqrt 2))
0.0ms	x	@	-inf	(/ (+ (* (* x x) (* x x)) 0) (* (* (* x (* x x)) x) (* x (+ x x))))
0.0ms	x	@	inf	(/ (+ (* (* x x) (* x x)) 0) (* (* (* x (* x x)) x) (* x (+ x x))))
0.0ms	x	@	0	(* x (exp (* (log 2) 1/2)))
0.0ms	x	@	0	(/ (+ (* (* x x) (* x x)) 0) (* (* (* x (* x x)) x) (* x (+ x x))))

simplify206.0ms (5.4%)

Memory

22.8MiB live, 137.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2 036×	`div-sub`
1 808×	`lower-*.f64`
1 808×	`lower-*.f32`
1 696×	`lower-fma.f64`
1 696×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	532
1	61	532
2	188	532
3	382	532
4	731	532
5	1093	532
6	1423	532
7	1547	532
8	1623	532
9	1706	532
10	1772	532
11	1982	532
12	2131	532
13	2178	532
14	2204	532
15	2218	532
16	2220	532
17	2220	532
18	2268	532
19	2704	532
20	4367	532
21	4965	532
22	5140	532
23	5303	532
24	5417	532
25	5521	532
26	6318	532
27	6600	532
28	7074	532
29	7550	532
30	7996	532
0	8176	532

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

rewrite69.0ms (1.8%)

Memory

-17.7MiB live, 99.8MiB allocated

Rules

166×	`lower-*.f32`
154×	`lower-*.f64`
154×	`lower-/.f64`
154×	`lower-/.f32`
142×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	145
0	49	77
1	139	38
0	1092	38

Stop Event

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

Counts

14 → 54

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

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

eval18.0ms (0.5%)

Memory: 8.8MiB live, 46.1MiB allocated
Compiler: Compiled 2 441 to 205 computations (91.6% saved)

prune11.0ms (0.3%)

Memory

-4.4MiB live, 34.9MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	190	8	198

Accuracy

100.0%

Counts

198 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
▶	16.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))
✓	53.2%	(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)))))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 71 to 41 computations (42.3% saved)

simplify310.0ms (8.1%)

Memory

-0.3MiB live, 326.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

6 316×	`lower-*.f32`
6 306×	`lower-*.f64`
4 730×	`lower-fma.f64`
4 730×	`lower-fma.f32`
1 896×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	106
0	20	102
1	44	52
2	168	42
3	931	40
4	2940	40
5	3423	40
6	4768	40
7	6136	40
8	7149	40
9	7529	40
10	7766	40
11	7945	40
0	8066	37

Stop Event

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

Calls

Call 1

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

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

localize41.0ms (1.1%)

Memory

-6.4MiB live, 76.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.06640625	(.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))
accuracy	0.3152931330160837	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))))
accuracy	29.92347126976054	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))
accuracy	49.91115814046572	(/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))

Samples

21.0ms

256×

valid

Compiler

Compiled 108 to 13 computations (88% saved)

Precisions

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

ival-mult: 7.0ms (51.7% of total)

ival-div: 3.0ms (22.2% of total)

ival-sqrt: 2.0ms (14.8% of total)

ival-add: 1.0ms (7.4% 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%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))>
#<alt (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))>
#<alt (.f64 (.f64 x (*.f64 x x)) x)>
#<alt (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))>

Outputs
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (/ 1/2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>

Calls

15 calls:

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

simplify8.0ms (0.2%)

Memory

13.9MiB live, 13.9MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	268
1	23	268
2	42	268
3	47	268
4	51	268
5	63	268
6	75	268
7	86	268
8	106	268
9	111	268
0	111	268

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

Inputs
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (pow x 2))
(/ 1/2 (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 (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 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)
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))
(* 2 (pow x 6))

Outputs
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
(/ 1/2 (pow x 2))
(/.f64 #s(literal 1/2 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))
(* 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 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))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(* 2 (pow x 6))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))

rewrite57.0ms (1.5%)

Memory

-2.6MiB live, 72.2MiB allocated

Rules

218×	`lower-*.f32`
208×	`lower-*.f64`
174×	`lower-/.f32`
170×	`lower-/.f64`
54×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	88
0	20	76
1	71	16
0	632	15

Stop Event

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

Counts

5 → 337

Calls

Call 1

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

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

eval78.0ms (2%)

Memory: 4.8MiB live, 83.3MiB allocated
Compiler: Compiled 6 912 to 869 computations (87.4% saved)

prune49.0ms (1.3%)

Memory

-18.3MiB live, 143.4MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	412	1	413
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	412	9	421

Accuracy

100.0%

Counts

421 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.1%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
✓	16.2%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))
	6.9%	(sqrt.f64 (+.f64 x x))
✓	53.2%	(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)))))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 203 to 82 computations (59.6% saved)

regimes17.0ms (0.5%)

Memory

-1.0MiB live, 38.0MiB allocated

Counts

12 → 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)))
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))))
(sqrt.f64 (/.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))))))
(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)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	(+.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)

regimes14.0ms (0.4%)

Memory

36.0MiB live, 36.0MiB allocated

Counts

10 → 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)))
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))))
(sqrt.f64 (/.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))))))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes12.0ms (0.3%)

Memory

-11.6MiB live, 25.6MiB 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:

5.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
99.3%	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)

regimes6.0ms (0.2%)

Memory

17.7MiB live, 17.7MiB 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:

2.0ms	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
6.9%	1	`x`
6.9%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
6.9%	1	`(+.f64 (.f64 x x) (.f64 x x))`
6.9%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes19.0ms (0.5%)

Memory

-35.1MiB live, 22.4MiB 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:

15.0ms	(*.f64 x x)
1.0ms	x
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

Accuracy	Segments	Branch
3.6%	1	`x`
3.6%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.6%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.6%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB 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)

soundness199.0ms (5.2%)

Memory

-21.4MiB live, 253.9MiB allocated

Rules

218×	`lower-*.f32`
208×	`lower-*.f64`
174×	`lower-/.f32`
170×	`lower-/.f64`
170×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	18
0	7	14
1	23	10
0	160	9
0	24	126
0	41	48
1	123	26
0	1078	26
0	11	88
0	20	76
1	71	16
0	632	15
0	30	145
0	49	77
1	139	38
0	1092	38
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
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 207 to 83 computations (59.9% saved)

preprocess65.0ms (1.7%)

Memory: 2.9MiB live, 79.2MiB 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	15	268
1	23	268
2	42	268
3	47	268
4	51	268
5	63	268
6	75	268
7	86	268
8	106	268
9	111	268
0	111	268

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	15	268
1	23	268
2	42	268
3	47	268
4	51	268
5	63	268
6	75	268
7	86	268
8	106	268
9	111	268
0	111	268

start0.0ms (0%)

analyze0.0ms (0%)

sample535.0ms (14%)

explain81.0ms (2.1%)

preprocess17.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize67.0ms (1.7%)

series3.0ms (0.1%)

simplify12.0ms (0.3%)

rewrite34.0ms (0.9%)

eval8.0ms (0.2%)

prune10.0ms (0.3%)

simplify501.0ms (13.1%)

localize129.0ms (3.4%)

series7.0ms (0.2%)

simplify218.0ms (5.7%)

rewrite69.0ms (1.8%)

eval37.0ms (1%)

prune14.0ms (0.4%)

simplify720.0ms (18.8%)

localize175.0ms (4.6%)

series4.0ms (0.1%)

simplify206.0ms (5.4%)

rewrite69.0ms (1.8%)

eval18.0ms (0.5%)

prune11.0ms (0.3%)

simplify310.0ms (8.1%)

localize41.0ms (1.1%)

series2.0ms (0%)

simplify8.0ms (0.2%)

rewrite57.0ms (1.5%)

eval78.0ms (2%)

prune49.0ms (1.3%)

regimes17.0ms (0.5%)

regimes14.0ms (0.4%)

regimes12.0ms (0.3%)

regimes6.0ms (0.2%)

regimes19.0ms (0.5%)

simplify5.0ms (0.1%)

soundness199.0ms (5.2%)

preprocess65.0ms (1.7%)

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	15	268
1	23	268
2	42	268
3	47	268
4	51	268
5	63	268
6	75	268
7	86	268
8	106	268
9	111	268
0	111	268