Metrics for sqrt E (should all be same)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample556.0ms (19.6%)

Memory

0.6MiB live, 739.4MiB allocated

Samples

364.0ms

8 256×

valid

Precisions

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

ival-pow2: 106.0ms (48.7% of total)

ival-sqrt: 62.0ms (28.5% of total)

ival-add: 41.0ms (18.8% of total)

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

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

Bogosity

preprocess21.0ms (0.7%)

Memory

-0.1MiB live, 39.0MiB allocated

Algorithm

1×	egg-herbie

Rules

58×	`associate-r`
54×	`unsub-neg`
38×	`distribute-rgt-neg-out`
38×	`distribute-lft-neg-out`
38×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Stop Event

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

Calls

Call 1

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

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

explain68.0ms (2.4%)

Memory

18.2MiB live, 101.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	2	(1.4097574924722788e-158)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	65	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	65
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	130
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	55	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	55
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	110

Confusion

	Predicted +	Predicted -
+	120	2
-	0	134

Precision

1.0

Recall

0.9836065573770492

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	2
-	0	0	134

Precision?

1.0

Recall?

0.9836065573770492

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sqrt: 7.0ms (44.9% of total)

ival-pow2: 6.0ms (38.5% of total)

ival-add: 2.0ms (12.8% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.1%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.2%)

Memory

5.5MiB live, 5.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
✓	cost-diff	320	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	20
0	8	16
1	10	16
2	15	16
3	18	16
0	18	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.7%)

Memory

-11.3MiB live, 26.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	accuracy	56.1%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

14.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-pow2: 5.0ms (57.4% of total)

ival-sqrt: 2.0ms (23% of total)

ival-add: 1.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

Outputs
#<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 (* 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)))>

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (+ (pow x 2) (pow x 2)))
1.0ms	x	@	inf	(sqrt (+ (pow x 2) (pow x 2)))
0.0ms	x	@	inf	(pow x 2)
0.0ms	x	@	0	(pow x 2)
0.0ms	x	@	0	(+ (pow x 2) (pow x 2))

rewrite38.0ms (1.3%)

Memory

4.5MiB live, 42.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

70×	`lower-*.f64`
70×	`lower-*.f32`
44×	`lower-fma.f64`
44×	`lower-fma.f32`
34×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	18
0	8	14
1	28	10
0	170	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

simplify8.0ms (0.3%)

Memory

10.3MiB live, 10.3MiB 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
(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)
(* 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)))

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

eval11.0ms (0.4%)

Memory: -21.9MiB live, 15.9MiB allocated
Compiler: Compiled 726 to 104 computations (85.7% saved)

prune8.0ms (0.3%)

Memory

16.8MiB live, 16.8MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Accuracy

100.0%

Counts

88 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
	19.2%	(/.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))))
▶	50.5%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	19.2%	(sqrt.f64 (/.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))))
▶	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	51.2%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 146 to 68 computations (53.4% saved)

simplify247.0ms (8.7%)

Memory

-2.3MiB live, 308.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	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 (.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))))
✓	cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	cost-diff	2944	(/.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)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(*.f64 x (+.f64 x x))
✓	cost-diff	0	(sqrt.f64 (*.f64 x (+.f64 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	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	5312	(hypot.f64 x x)

Rules

7 134×	`lower-*.f32`
7 126×	`lower-*.f64`
6 422×	`lower-fma.f32`
6 420×	`lower-fma.f64`
1 622×	`lower-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	122
0	29	78
1	51	74
2	179	68
3	846	66
4	1756	66
5	2778	66
6	3945	66
7	5872	66
0	8217	66

Stop Event

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

Calls

Call 1

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

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

localize189.0ms (6.7%)

Memory

-12.1MiB live, 114.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	56.1%	(sqrt.f64 (/.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))))
✓	accuracy	25.0%	(/.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)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 x (+.f64 x x))
✓	accuracy	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(hypot.f64 x x)

Samples

48.0ms

256×

valid

Compiler

Compiled 135 to 18 computations (86.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 10.0ms (34.5% of total)

ival-sqrt: 7.0ms (24.1% of total)

ival-hypot: 6.0ms (20.7% of total)

ival-add: 3.0ms (10.3% of total)

ival-div: 2.0ms (6.9% of total)

ival-neg: 1.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

11 → 120

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>
#<alt (*.f64 x (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))>
#<alt (sqrt.f64 (*.f64 x (+.f64 x x)))>
#<alt (*.f64 x (+.f64 x x))>
#<alt (+.f64 x x)>
#<alt (/.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)))>
#<alt (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))>
#<alt (sqrt.f64 (/.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))))>
#<alt (.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 (* 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 (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* 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 (* 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 (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>
#<alt (* 2 (pow x 6))>

Calls

30 calls:

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

rewrite52.0ms (1.8%)

Memory

22.4MiB live, 59.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

182×	`lower-*.f32`
178×	`lower-*.f64`
170×	`lower-/.f64`
170×	`lower-/.f32`
150×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	97
0	29	37
1	105	21
0	974	21

Stop Event

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

Counts

11 → 51

Calls

Call 1

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

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

simplify20.0ms (0.7%)

Memory

-20.2MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	516
1	23	516
2	38	516
3	42	516
4	46	516
5	58	516
6	70	516
7	81	516
8	101	516
9	106	516
0	106	516

Stop Event

1×	iter limit
1×	saturated

Counts

120 → 120

Calls

Call 1

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

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

eval24.0ms (0.8%)

Memory: 10.6MiB live, 47.7MiB allocated
Compiler: Compiled 3 893 to 248 computations (93.6% saved)

prune16.0ms (0.6%)

Memory

-8.0MiB live, 30.0MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	251	9	260

Accuracy

100.0%

Counts

260 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	30.8%	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	19.2%	(/.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))))
✓	50.5%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	50.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
▶	19.2%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	51.2%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	3.9%	#s(literal 0 binary64)

Compiler

Compiled 180 to 91 computations (49.4% saved)

simplify245.0ms (8.6%)

Memory

-0.6MiB live, 314.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	cost-diff	704	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	cost-diff	1280	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
✓	cost-diff	1664	(/.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	(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	192	(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	1216	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	1728	(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
✓	cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	cost-diff	64	(sqrt.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
✓	cost-diff	2944	(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
✓	cost-diff	0	(log.f64 #s(literal 2 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	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

5 468×	`lower-*.f32`
5 454×	`lower-*.f64`
4 352×	`lower-fma.f32`
4 350×	`lower-fma.f64`
2 912×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	246
0	46	267
1	93	216
2	359	121
3	1735	113
4	3324	113
5	5262	113
0	8839	109

Stop Event

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

Calls

Call 1

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

localize98.0ms (3.4%)

Memory

12.0MiB live, 180.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	84.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	accuracy	77.0%	(sqrt.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)))
✓	accuracy	37.9%	(/.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	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.6%	(.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	55.8%	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (+.f64 #s(literal 0 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	99.8%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	56.1%	(sqrt.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (.f64 (.f64 x x) (*.f64 x x))))
✓	accuracy	25.0%	(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))) (.f64 (.f64 x x) (*.f64 x x)))
✓	accuracy	100.0%	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	98.4%	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

52.0ms

256×

valid

Compiler

Compiled 258 to 27 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 12.0ms (32.8% of total)

ival-sqrt: 9.0ms (24.6% of total)

ival-div: 4.0ms (10.9% of total)

ival-log: 4.0ms (10.9% of total)

ival-add: 3.0ms (8.2% of total)

ival-exp: 3.0ms (8.2% of total)

ival-sub: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

7.2MiB live, 7.2MiB allocated

Counts

18 → 168

Calls

Call 1

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

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

Calls

42 calls:

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

rewrite56.0ms (2%)

Memory

-6.4MiB live, 31.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

218×	`lower-*.f32`
212×	`lower-*.f64`
212×	`lower-/.f64`
212×	`lower-/.f32`
114×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	191
0	46	70
1	173	31
0	1585	31

Stop Event

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

Counts

18 → 90

Calls

Call 1

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

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

simplify76.0ms (2.7%)

Memory

-6.2MiB live, 37.0MiB allocated

Algorithm

1×	egg-herbie

Rules

196×	`lower-*.f64`
196×	`lower-*.f32`
192×	`lower-fma.f64`
192×	`lower-fma.f32`
82×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732

Stop Event

1×	iter limit
1×	saturated

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

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

eval35.0ms (1.2%)

Memory: 6.8MiB live, 80.1MiB allocated
Compiler: Compiled 7 739 to 413 computations (94.7% saved)

prune21.0ms (0.7%)

Memory

14.7MiB live, 52.3MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	381	2	383
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	384	8	392

Accuracy

100.0%

Counts

392 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	30.8%	(/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	20.3%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))
✓	50.5%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	50.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	51.2%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 65 to 43 computations (33.8% saved)

simplify324.0ms (11.4%)

Memory

11.6MiB live, 478.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal -2 binary64))
✓	cost-diff	192	(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	640	(/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 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)))) (*.f64 x x))
✓	cost-diff	64	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))

Rules

6 274×	`lower-*.f32`
6 264×	`lower-*.f64`
4 600×	`lower-fma.f32`
4 598×	`lower-fma.f64`
2 040×	`distribute-lft-out`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	105
0	29	97
1	52	89
2	130	71
3	279	65
4	431	65
5	1114	65
6	2003	65
7	2493	65
8	2786	65
9	3693	65
10	4157	65
11	4737	65
12	5493	65
13	6399	65
14	7053	65
15	7456	65
16	7676	65
17	7870	65
0	8026	65

Stop Event

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

Calls

Call 1

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

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

localize57.0ms (2%)

Memory

3.8MiB live, 125.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal -2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	55.8%	(/.f64 (.f64 (.f64 x x) #s(literal -2 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.9%	(.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	84.8%	(sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	accuracy	37.9%	(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))) (*.f64 x x))

Samples

36.0ms

256×

valid

Compiler

Compiled 111 to 19 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 14.0ms (52.1% of total)

ival-sqrt: 5.0ms (18.6% of total)

ival-div: 3.0ms (11.2% of total)

ival-add: 3.0ms (11.2% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

-27.9MiB live, 9.2MiB allocated

Counts

10 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

rewrite74.0ms (2.6%)

Memory

30.1MiB live, 105.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

348×	`lower-*.f32`
342×	`lower-*.f64`
328×	`lower-/.f32`
324×	`lower-/.f64`
156×	`lower-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	88
0	29	73
1	110	35
0	917	35

Stop Event

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

Counts

10 → 126

Calls

Call 1

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

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

simplify18.0ms (0.6%)

Memory

-11.9MiB live, 27.2MiB allocated

Algorithm

1×	egg-herbie

Rules

142×	`lower-*.f64`
142×	`lower-*.f32`
138×	`lower-fma.f64`
138×	`lower-fma.f32`
72×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	488
1	38	488
2	76	488
3	127	488
4	147	488
5	188	488
6	222	488
7	251	488
8	294	488
9	306	488
10	307	488
0	307	488

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

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

eval33.0ms (1.2%)

Memory: -13.7MiB live, 68.5MiB allocated
Compiler: Compiled 4 328 to 385 computations (91.1% saved)

prune48.0ms (1.7%)

Memory

7.2MiB live, 46.2MiB allocated

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	278	4	282
Fresh	0	0	0
Picked	2	0	2
Done	0	6	6
Total	280	10	290

Accuracy

100.0%

Counts

290 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
	16.4%	(/.f64 (.f64 x (.f64 x (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
	20.3%	(/.f64 (sqrt.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x (+.f64 x x)))) (.f64 x x))
	51.2%	(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) x))
	51.1%	(*.f64 x (/.f64 #s(literal -2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	50.5%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	50.3%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	56.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	51.2%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	3.9%	#s(literal 0 binary64)

Compiler

Compiled 284 to 106 computations (62.7% saved)

regimes23.0ms (0.8%)

Memory

18.0MiB live, 18.0MiB allocated

Counts

17 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

6.0ms	x
5.0ms	(pow.f64 x #s(literal 2 binary64))
5.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
5.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes51.0ms (1.8%)

Memory

-22.0MiB live, 16.3MiB allocated

Counts

14 → 2

Calls

Call 1

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

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

Calls

4 calls:

37.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
5.0ms	x
4.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
78.2%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
78.2%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
78.2%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes4.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
50.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
50.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
50.5%	1	`(pow.f64 x #s(literal 2 binary64))`
50.5%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes5.0ms (0.2%)

Memory

10.7MiB live, 10.7MiB 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 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
3.9%	1	`x`
3.9%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.9%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.9%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch14.0ms (0.5%)

Memory

-18.5MiB live, 19.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Samples

6.0ms

144×

valid

Compiler

Compiled 174 to 134 computations (23% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-add: 1.0ms (30.1% of total)

ival-sqrt: 1.0ms (30.1% of total)

ival-pow2: 1.0ms (30.1% of total)

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

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

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.4256916573461186e-307	7.534118243227063e-305

Compiler

Compiled 129 to 107 computations (17.1% saved)

simplify7.0ms (0.2%)

Memory

14.7MiB live, 14.7MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	39
1	26	39
2	35	39
3	40	39
4	42	39

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 0 binary64)

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal -2 binary64)) x)) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x)) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(literal 0 binary64)

soundness178.0ms (6.3%)

Memory

-19.3MiB live, 234.9MiB allocated

Rules

348×	`lower-*.f32`
342×	`lower-*.f64`
328×	`lower-/.f32`
324×	`lower-/.f64`
196×	`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
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732
0	15	97
0	29	37
1	105	21
0	974	21
0	16	88
0	29	73
1	110	35
0	917	35
0	5	18
0	8	14
1	28	10
0	170	9

Stop Event

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

Compiler

Compiled 120 to 72 computations (40% saved)

preprocess167.0ms (5.9%)

Memory: -6.2MiB live, 70.7MiB allocated
Compiler: Compiled 98 to 44 computations (55.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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

Iter	Nodes	Cost
0	14	516
1	23	516
2	38	516
3	42	516
4	46	516
5	58	516
6	70	516
7	81	516
8	101	516
9	106	516
0	106	516

Iter	Nodes	Cost
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732

Iter	Nodes	Cost
0	20	488
1	38	488
2	76	488
3	127	488
4	147	488
5	188	488
6	222	488
7	251	488
8	294	488
9	306	488
10	307	488
0	307	488

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732
0	15	97
0	29	37
1	105	21
0	974	21
0	16	88
0	29	73
1	110	35
0	917	35
0	5	18
0	8	14
1	28	10
0	170	9

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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

Iter	Nodes	Cost
0	14	516
1	23	516
2	38	516
3	42	516
4	46	516
5	58	516
6	70	516
7	81	516
8	101	516
9	106	516
0	106	516

Iter	Nodes	Cost
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732

Iter	Nodes	Cost
0	20	488
1	38	488
2	76	488
3	127	488
4	147	488
5	188	488
6	222	488
7	251	488
8	294	488
9	306	488
10	307	488
0	307	488

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732
0	15	97
0	29	37
1	105	21
0	974	21
0	16	88
0	29	73
1	110	35
0	917	35
0	5	18
0	8	14
1	28	10
0	170	9

analyze0.0ms (0%)

sample556.0ms (19.6%)

preprocess21.0ms (0.7%)

explain68.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize21.0ms (0.7%)

series3.0ms (0.1%)

rewrite38.0ms (1.3%)

simplify8.0ms (0.3%)

eval11.0ms (0.4%)

prune8.0ms (0.3%)

simplify247.0ms (8.7%)

localize189.0ms (6.7%)

series4.0ms (0.1%)

rewrite52.0ms (1.8%)

simplify20.0ms (0.7%)

eval24.0ms (0.8%)

prune16.0ms (0.6%)

simplify245.0ms (8.6%)

localize98.0ms (3.4%)

series5.0ms (0.2%)

rewrite56.0ms (2%)

simplify76.0ms (2.7%)

eval35.0ms (1.2%)

prune21.0ms (0.7%)

simplify324.0ms (11.4%)

localize57.0ms (2%)

series6.0ms (0.2%)

rewrite74.0ms (2.6%)

simplify18.0ms (0.6%)

eval33.0ms (1.2%)

prune48.0ms (1.7%)

regimes23.0ms (0.8%)

regimes51.0ms (1.8%)

regimes4.0ms (0.1%)

regimes7.0ms (0.2%)

regimes5.0ms (0.2%)

bsearch14.0ms (0.5%)

bsearch1.0ms (0%)

simplify7.0ms (0.2%)

soundness178.0ms (6.3%)

preprocess167.0ms (5.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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

Iter	Nodes	Cost
0	14	516
1	23	516
2	38	516
3	42	516
4	46	516
5	58	516
6	70	516
7	81	516
8	101	516
9	106	516
0	106	516

Iter	Nodes	Cost
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732

Iter	Nodes	Cost
0	20	488
1	38	488
2	76	488
3	127	488
4	147	488
5	188	488
6	222	488
7	251	488
8	294	488
9	306	488
10	307	488
0	307	488

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	20	780
1	41	732
2	98	732
3	190	732
4	239	732
5	305	732
6	355	732
7	398	732
8	427	732
9	427	732
0	427	732
0	15	97
0	29	37
1	105	21
0	974	21
0	16	88
0	29	73
1	110	35
0	917	35
0	5	18
0	8	14
1	28	10
0	170	9