Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample1.3s (41%)

Memory

-0.2MiB live, 612.4MiB allocated

Samples

317.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-hypot: 158.0ms (94.2% of total)

ival-true: 6.0ms (3.6% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain66.0ms (2.1%)

Memory

-3.1MiB live, 117.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
119	-	2	(-1.9459335138386085e-159)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	59	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	59
↳	`(*.f64 x x)`	underflow	118
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	58	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	58
↳	`(*.f64 x x)`	overflow	116

Confusion

	Predicted +	Predicted -
+	117	2
-	0	137

Precision

1.0

Recall

0.9831932773109243

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	2
-	0	0	137

Precision?

1.0

Recall?

0.9831932773109243

Freqs

test

number	freq
0	139
1	117

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

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: 9.0ms (51.6% of total)

ival-mult: 6.0ms (34.4% of total)

ival-add: 2.0ms (11.5% of total)

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

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

preprocess20.0ms (0.6%)

Memory

-5.2MiB live, 31.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 9 to 4 computations (55.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.3%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB 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

localize22.0ms (0.7%)

Memory

0.3MiB live, 36.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 (.f64 x x) (.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	27.318734222241872	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

17.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-hypot: 5.0ms (65.2% of total)

ival-mult: 2.0ms (26.1% of total)

ival-add: 1.0ms (13% of total)

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

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

series3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB 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)))
1.0ms	x	@	0	(+ (* x x) (* x x))
0.0ms	x	@	inf	(+ (* x x) (* x x))
0.0ms	x	@	-inf	(+ (* x x) (* x x))

simplify6.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB 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)

rewrite42.0ms (1.3%)

Memory

-21.8MiB live, 69.5MiB 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 (0.3%)

Memory: 21.5MiB live, 21.5MiB allocated
Compiler: Compiled 750 to 94 computations (87.5% saved)

prune72.0ms (2.2%)

Memory

-12.1MiB live, 26.9MiB 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)
▶	19.4%	(/.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))))
▶	99.3%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	57.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 102 to 50 computations (51% saved)

simplify19.0ms (0.6%)

Memory

7.7MiB live, 46.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.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))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
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

352×	`lower-*.f32`
340×	`lower-*.f64`
308×	`lower-fma.f32`
306×	`lower-fma.f64`
294×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Stop Event

1×	iter limit
1×	saturated
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)
(/.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))))
(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
(.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 x (+.f64 x x))
(+.f64 x x)
(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))

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

localize72.0ms (2.2%)

Memory

13.1MiB live, 169.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	16.279645341450717	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.17185978894967	(/.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))))
accuracy	0	(+.f64 x x)
accuracy	0	(sqrt.f64 (+.f64 x x))
accuracy	0	(sqrt.f64 x)
accuracy	0.42578125	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
accuracy	0	(+.f64 x x)
accuracy	0	(*.f64 (+.f64 x x) x)
accuracy	27.318734222241872	(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	0.3984375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.015625	(hypot.f64 x x)

Samples

47.0ms

256×

valid

Compiler

Compiled 149 to 22 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 16.0ms (47.7% of total)

ival-sqrt: 9.0ms (26.8% of total)

ival-hypot: 4.0ms (11.9% of total)

ival-add: 2.0ms (6% of total)

ival-div: 1.0ms (3% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

-16.9MiB live, 21.6MiB 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 (sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))>
#<alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))>
#<alt (/.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))))>
#<alt (sqrt.f64 (.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 (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)>
#<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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>

Calls

39 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(* (+ x x) x)
1.0ms	x	@	-inf	(* (sqrt x) (sqrt (+ x x)))
0.0ms	x	@	0	(sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x))))
0.0ms	x	@	0	(+ x x)
0.0ms	x	@	-inf	(sqrt (+ x x))

simplify230.0ms (7.1%)

Memory

9.7MiB live, 126.7MiB allocated

Algorithm

1×	egg-herbie

Rules

1 808×	`lower-*.f64`
1 808×	`lower-fma.f64`
1 808×	`lower-fma.f32`
1 808×	`lower-*.f32`
1 768×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	664
1	63	664
2	168	664
3	337	664
4	579	664
5	920	664
6	1535	664
7	1673	664
8	1758	664
9	1845	664
10	1911	664
11	1956	664
12	1972	664
13	1976	664
14	1976	664
15	2080	664
16	2339	664
17	2781	664
18	3397	664
19	3463	664
20	3577	664
21	3635	664
22	3695	664
23	4027	664
24	4163	664
25	4163	664
26	4163	664
27	4163	664
28	4639	664
29	4811	664
30	4847	664
31	4861	664
32	4863	664
33	4863	664
34	5067	664
0	5067	664

Stop Event

1×	iter limit
1×	saturated

Counts

156 → 156

Calls

Call 1

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

rewrite99.0ms (3.1%)

Memory

13.1MiB live, 91.3MiB allocated

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29

Stop Event

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

Counts

14 → 60

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

eval29.0ms (0.9%)

Memory: 12.1MiB live, 82.0MiB allocated
Compiler: Compiled 4 677 to 286 computations (93.9% saved)

prune26.0ms (0.8%)

Memory

-37.2MiB live, 54.4MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	276	5	281
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	277	9	286

Accuracy

100.0%

Counts

286 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.6%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
▶	19.4%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
▶	26.5%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
✓	99.3%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	57.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	99.0%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 179 to 97 computations (45.8% saved)

simplify20.0ms (0.6%)

Memory

10.9MiB live, 50.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
cost-diff	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	0	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
cost-diff	0	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
cost-diff	0	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
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

400×	`lower-*.f32`
382×	`lower-*.f64`
324×	`associate-r`
308×	`lower-fma.f32`
306×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	324
0	64	275
1	94	222
2	157	197
3	244	181
4	336	181
5	618	181
6	653	181
7	654	181
0	654	178

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize136.0ms (4.2%)

Memory

3.0MiB live, 232.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
accuracy	16.279645341450703	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.17185978894967	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	0.3984375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	16.279645341450703	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
accuracy	40.17185978894967	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 0 binary64))))
accuracy	0.049160009768442016	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
accuracy	0.170253759768442	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
accuracy	40.17185978894967	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.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	0.3984375	(.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

66.0ms

256×

valid

Compiler

Compiled 306 to 29 computations (90.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 16.0ms (33.4% of total)

ival-sqrt: 9.0ms (18.8% of total)

ival-exp: 7.0ms (14.6% of total)

ival-hypot: 7.0ms (14.6% of total)

ival-div: 3.0ms (6.3% of total)

ival-log: 3.0ms (6.3% of total)

ival-add: 2.0ms (4.2% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

15 → 144

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

Calls

36 calls:

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

simplify14.0ms (0.4%)

Memory

14.8MiB live, 14.8MiB allocated

Algorithm

1×	egg-herbie

Rules

122×	`lower-*.f64`
122×	`lower-*.f32`
118×	`lower-fma.f64`
118×	`lower-fma.f32`
56×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	664
1	30	664
2	63	664
3	113	664
4	132	664
5	173	664
6	207	664
7	236	664
8	266	664
9	268	664
0	268	664

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 144

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

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

rewrite61.0ms (1.9%)

Memory

-23.2MiB live, 57.3MiB allocated

Rules

200×	`lower-*.f32`
186×	`lower-*.f64`
176×	`lower-/.f32`
172×	`lower-/.f64`
128×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	209
0	64	134
1	160	64
0	951	64

Stop Event

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

Counts

15 → 86

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

eval29.0ms (0.9%)

Memory: 20.6MiB live, 56.9MiB allocated
Compiler: Compiled 6 182 to 356 computations (94.2% saved)

prune32.0ms (1%)

Memory

-21.1MiB live, 61.8MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	331	3	334
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	334	9	343

Accuracy

100.0%

Counts

343 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	20.6%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
▶	35.0%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (fabs.f64 (.f64 x x)))
▶	35.0%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	57.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.0%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 86 to 49 computations (43% saved)

simplify16.0ms (0.5%)

Memory

28.7MiB live, 28.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

400×	`associate-r`
396×	`lower-*.f32`
378×	`lower-*.f64`
308×	`lower-fma.f64`
308×	`lower-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	277
0	46	231
1	77	191
2	152	177
3	399	163
4	617	163
5	618	163
0	618	163

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize91.0ms (2.8%)

Memory

-28.4MiB live, 143.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(.f64 (.f64 x (*.f64 x x)) x)
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	9.003394271051118	(sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))
accuracy	40.17185978894967	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
accuracy	0	#s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.1015625	(.f64 x (.f64 x x))
accuracy	0.171875	(.f64 (.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	40.17185978894967	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (fabs.f64 (.f64 x x)))
accuracy	0.078125	(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
accuracy	0.1171875	(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.3984375	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	40.17185978894967	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))

Samples

58.0ms

256×

valid

Compiler

Compiled 227 to 26 computations (88.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 24.0ms (52.1% of total)

ival-add: 9.0ms (19.5% of total)

ival-sqrt: 7.0ms (15.2% of total)

ival-div: 4.0ms (8.7% of total)

ival-fabs: 1.0ms (2.2% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))>
#<alt #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))>
#<alt (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (fabs.f64 (*.f64 x x))>
#<alt (/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (fabs.f64 (.f64 x x)))>
#<alt #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (.f64 x (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))>
#<alt (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x))))>
#<alt (.f64 (.f64 (.f64 x (.f64 x x)) x) (*.f64 x (+.f64 x x)))>
#<alt (.f64 (.f64 x (*.f64 x x)) x)>
#<alt (*.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (* (pow x 2) (sqrt 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (fabs (pow x 2))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))>
#<alt (* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))>
#<alt (* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))>
#<alt (* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))>
#<alt (* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (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 (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* (pow x 3) (sqrt 2))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<alt (* -1 (* (pow x 3) (sqrt 2)))>
#<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))>
#<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 (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

42 calls:

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

simplify201.0ms (6.2%)

Memory

-8.9MiB live, 223.3MiB allocated

Algorithm

1×	egg-herbie

Rules

3 724×	`lower-*.f64`
3 724×	`lower-*.f32`
2 136×	`lower-fma.f64`
2 136×	`lower-fma.f32`
1 730×	`div-sub`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	828
1	40	816
2	100	816
3	314	816
4	1424	816
5	2378	816
6	3853	816
7	5761	816
0	8344	816

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

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)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(* (pow x 2) (sqrt 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(fabs (pow x 2))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (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)))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* (pow x 3) (sqrt 2))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* -1 (* (pow x 3) (sqrt 2)))
(* 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))
(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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(* 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 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 2) (sqrt 2))
(.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(fabs (pow x 2))
(*.f64 x x)
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2)))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (/ (* (pow x 3) (sqrt 2)) (fabs (pow x 2))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.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))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (sqrt 2))
(.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* -1 (* (pow x 3) (sqrt 2)))
(neg.f64 (.f64 x (.f64 x (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(* 2 (pow x 6))
(.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.f64 x x)))
(pow x 4)
(.f64 x (.f64 x (*.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)))
(* 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)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

rewrite220.0ms (6.8%)

Memory

26.3MiB live, 219.3MiB allocated

Rules

3 940×	`lower-fma.f64`
3 940×	`lower-fma.f32`
2 306×	`lower-*.f32`
2 298×	`lower-*.f64`
1 262×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	218
0	46	181
1	131	63
2	701	43
3	5978	43
0	8068	43

Stop Event

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

Counts

14 → 545

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (.f64 x x)) #s(approx (sqrt ( (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) #s(literal 0 binary64))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x))))
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(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) x))
(.f64 (.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 12 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3/2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 6 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 6 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/4 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 x x)) #s(literal 1 binary64)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 3/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 6 binary64)))
(fabs.f64 (.f64 x (.f64 x x)))
(fabs.f64 (.f64 (.f64 x x) (neg.f64 x)))
(fabs.f64 (.f64 (neg.f64 x) (.f64 x x)))
(sqrt.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (*.f64 x x))
(/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 3/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/4 binary64))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 3/8 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (*.f64 x (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))) #s(literal -3/4 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(.f64 (sqrt.f64 x) (.f64 x (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (sqrt.f64 x)) (*.f64 x (sqrt.f64 x)))
(.f64 (.f64 x (*.f64 x (sqrt.f64 x))) (sqrt.f64 x))

eval108.0ms (3.3%)

Memory: -18.2MiB live, 194.6MiB allocated
Compiler: Compiled 19 594 to 2 032 computations (89.6% saved)

prune85.0ms (2.6%)

Memory

-2.5MiB live, 193.2MiB allocated

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	760	3	763
Fresh	0	0	0
Picked	2	1	3
Done	0	6	6
Total	762	10	772

Accuracy

100.0%

Counts

772 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	20.6%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) #s(approx (sqrt (+ ( (* x x) (* x x)) 0)) (*.f64 x x)))
	20.5%	(/.f64 (sqrt.f64 #s(approx (* (* (* x (* x x)) x) (* x (+ x x))) (.f64 #s(literal 2 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(approx (sqrt (+ (* (* x x) (* x x)) 0)) (*.f64 x x)))
	26.4%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (sqrt.f64 x)) (*.f64 x (sqrt.f64 x))))
	35.0%	(/.f64 #s(approx (sqrt (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))) (.f64 (.f64 x (.f64 x x)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x))
✓	99.3%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	57.3%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	99.4%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	99.0%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 349 to 110 computations (68.5% saved)

regimes23.0ms (0.7%)

Memory

1.3MiB live, 39.2MiB allocated

Counts

17 → 1

Calls

Call 1

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

6.0ms	(+.f64 (.f64 x x) (.f64 x x))
5.0ms	x
5.0ms	(*.f64 x x)
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes21.0ms (0.6%)

Memory

-2.1MiB live, 36.0MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
5.0ms	x
4.0ms	(*.f64 x x)
4.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes5.0ms (0.2%)

Memory

12.5MiB live, 12.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify5.0ms (0.2%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	11	17

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness80.0ms (2.5%)

Memory

-20.9MiB live, 95.8MiB allocated

Rules

168×	`lower-*.f32`
164×	`lower-*.f64`
134×	`lower-fma.f32`
132×	`lower-fma.f64`
112×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 44 to 23 computations (47.7% saved)

preprocess25.0ms (0.8%)

Memory: 18.6MiB live, 56.6MiB allocated
Remove: (abs x)
Compiler: Compiled 46 to 24 computations (47.8% 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	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	39	324
0	64	275
1	94	222
2	157	197
3	244	181
4	336	181
5	618	181
6	653	181
7	654	181
0	654	178

Iter	Nodes	Cost
0	16	664
1	30	664
2	63	664
3	113	664
4	132	664
5	173	664
6	207	664
7	236	664
8	266	664
9	268	664
0	268	664

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

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	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	39	324
0	64	275
1	94	222
2	157	197
3	244	181
4	336	181
5	618	181
6	653	181
7	654	181
0	654	178

Iter	Nodes	Cost
0	16	664
1	30	664
2	63	664
3	113	664
4	132	664
5	173	664
6	207	664
7	236	664
8	266	664
9	268	664
0	268	664

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (41%)

explain66.0ms (2.1%)

preprocess20.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize22.0ms (0.7%)

series3.0ms (0.1%)

simplify6.0ms (0.2%)

rewrite42.0ms (1.3%)

eval8.0ms (0.3%)

prune72.0ms (2.2%)

simplify19.0ms (0.6%)

localize72.0ms (2.2%)

series8.0ms (0.3%)

simplify230.0ms (7.1%)

rewrite99.0ms (3.1%)

eval29.0ms (0.9%)

prune26.0ms (0.8%)

simplify20.0ms (0.6%)

localize136.0ms (4.2%)

series3.0ms (0.1%)

simplify14.0ms (0.4%)

rewrite61.0ms (1.9%)

eval29.0ms (0.9%)

prune32.0ms (1%)

simplify16.0ms (0.5%)

localize91.0ms (2.8%)

series5.0ms (0.1%)

simplify201.0ms (6.2%)

rewrite220.0ms (6.8%)

eval108.0ms (3.3%)

prune85.0ms (2.6%)

regimes23.0ms (0.7%)

regimes21.0ms (0.6%)

regimes5.0ms (0.2%)

simplify5.0ms (0.2%)

soundness80.0ms (2.5%)

preprocess25.0ms (0.8%)

end0.0ms (0%)

Profiling

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

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

Iter	Nodes	Cost
0	23	136
0	40	122
1	55	110
2	102	95
3	188	89
4	253	89
5	522	89
6	557	89
7	558	89
0	558	89

Iter	Nodes	Cost
0	39	324
0	64	275
1	94	222
2	157	197
3	244	181
4	336	181
5	618	181
6	653	181
7	654	181
0	654	178

Iter	Nodes	Cost
0	16	664
1	30	664
2	63	664
3	113	664
4	132	664
5	173	664
6	207	664
7	236	664
8	266	664
9	268	664
0	268	664

Iter	Nodes	Cost
0	23	101
0	40	51
1	109	29
0	828	29
0	4	18
0	7	14
1	23	10
0	160	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148