Metrics for sqrt E (should all be same)

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample518.0ms (7.9%)

Memory

10.7MiB live, 717.0MiB allocated

Samples

354.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-pow2: 91.0ms (44.2% of total)

ival-sqrt: 71.0ms (34.5% of total)

ival-add: 37.0ms (18% of total)

ival-true: 5.0ms (2.4% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

preprocess19.0ms (0.3%)

Memory

-4.2MiB live, 34.9MiB allocated

Algorithm

2×	egg-herbie

Rules

52×	`unsub-neg`
50×	`associate-r`
30×	`distribute-rgt-neg-out`
26×	`distribute-lft-neg-out`
26×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	19
2	43	19
3	146	19
4	261	19
5	290	19
6	292	19
0	5	6
1	7	6
2	12	6
3	15	6
0	15	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (pow x 2) (pow x 2)))

Outputs
(sqrt (+ (pow x 2) (pow x 2)))
(sqrt.f64 (*.f64 x (+.f64 x x)))

Call 2

Inputs
(sqrt (+ (pow x 2) (pow x 2)))
(sqrt (+ (pow (neg x) 2) (pow (neg x) 2)))
(neg (sqrt (+ (pow (neg x) 2) (pow (neg x) 2))))

Outputs
(sqrt (+ (pow x 2) (pow x 2)))
(sqrt (* x (+ x x)))
(sqrt (+ (pow (neg x) 2) (pow (neg x) 2)))
(sqrt (* x (+ x x)))
(neg (sqrt (+ (pow (neg x) 2) (pow (neg x) 2))))
(neg (sqrt (* x (+ x x))))

Symmetry

(abs x)

explain67.0ms (1%)

Memory

28.5MiB live, 105.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	1	(1.489304771835313e-161)	`(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))))`	oflow-rescue	70	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	70
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	140
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	61	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	61
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	122

Confusion

	Predicted +	Predicted -
+	131	1
-	0	124

Precision

1.0

Recall

0.9924242424242424

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	1
-	0	0	124

Precision?

1.0

Recall?

0.9924242424242424

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 5.0ms (42.8% of total)

ival-sqrt: 3.0ms (25.7% of total)

ival-add: 2.0ms (17.1% 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: 0.4MiB live, 0.4MiB 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
▶	51.9%	(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 (0.1%)

Memory

4.7MiB live, 4.7MiB 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×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
4×	`+-lowering-+.f64`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	7	16
2	12	16
3	15	16
0	15	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (pow x 2) (pow x 2)))
(+ (pow x 2) (pow x 2))
(pow x 2)
x
2

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

localize21.0ms (0.3%)

Memory

-15.9MiB live, 27.2MiB 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	51.9%	(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-add: 4.0ms (45.6% of total)

ival-pow2: 3.0ms (34.2% of total)

ival-sqrt: 2.0ms (22.8% 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%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (pow x 2)>
#<alt (+ (pow x 2) (pow x 2))>
#<alt (sqrt (+ (pow x 2) (pow x 2)))>

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 (0.6%)

Memory

8.7MiB live, 46.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

70×	`-lowering-.f32`
70×	`-lowering-.f64`
44×	`accelerator-lowering-fma.f32`
44×	`accelerator-lowering-fma.f64`
34×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
1	25	10
0	167	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

Inputs
(pow x 2)
(+ (pow x 2) (pow x 2))
(sqrt (+ (pow x 2) (pow x 2)))

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

simplify13.0ms (0.2%)

Memory

-23.4MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`-lowering-.f32`
38×	`-lowering-.f64`
38×	`accelerator-lowering-fma.f32`
38×	`accelerator-lowering-fma.f64`
36×	`+-lowering-+.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)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(pow x 2)
(fma.f64 x x #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* 2 (pow x 2))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* x (sqrt 2))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
(* -1 (* x (sqrt 2)))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))

eval8.0ms (0.1%)

Memory: 15.8MiB live, 15.8MiB allocated
Compiler: Compiled 790 to 110 computations (86.1% saved)

prune6.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	3	88

Accuracy

100.0%

Counts

88 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
▶	100.0%	(hypot.f64 x x)
▶	51.9%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify6.0ms (0.1%)

Memory

-32.9MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

18×	`-lowering-.f32`
18×	`-lowering-.f64`
8×	`*-commutative`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	17	31
2	21	31
0	21	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (* x (+ x x)))
(* x (+ x x))
x
(+ x x)
(sqrt (+ (* x x) (* x x)))
x
(+ (* x (sqrt 2)) 0)
x
(sqrt 2)
2
0

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

localize34.0ms (0.5%)

Memory

5.6MiB live, 46.4MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.2%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
✓	accuracy	100.0%	(hypot.f64 x x)
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 x (+.f64 x x))
✓	accuracy	51.9%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Samples

24.0ms

256×

valid

Compiler

Compiled 31 to 12 computations (61.3% saved)

Precisions

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

ival-add: 6.0ms (37% of total)

ival-hypot: 4.0ms (24.7% of total)

ival-mult: 3.0ms (18.5% of total)

ival-sqrt: 3.0ms (18.5% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

6 → 60

Calls

Call 1

Inputs
#<alt (sqrt (* x (+ x x)))>
#<alt (* x (+ x x))>
#<alt (+ x x)>
#<alt (sqrt (+ (* x x) (* x x)))>
#<alt (+ (* x (sqrt 2)) 0)>
#<alt (sqrt 2)>

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

Calls

15 calls:

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

rewrite55.0ms (0.8%)

Memory

23.6MiB live, 61.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

796×	`frac-times`
348×	`times-frac`
292×	`-lowering-.f32`
292×	`-lowering-.f64`
182×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	52	7
2	418	7
0	4043	7

Stop Event

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

Counts

6 → 12

Calls

Call 1

Inputs
(sqrt (* x (+ x x)))
(* x (+ x x))
(+ x x)
(sqrt (+ (* x x) (* x x)))
(+ (* x (sqrt 2)) 0)
(sqrt 2)

Outputs
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
#s(literal 0 binary64)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.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)))

simplify14.0ms (0.2%)

Memory

-20.0MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`-lowering-.f32`
38×	`-lowering-.f64`
38×	`accelerator-lowering-fma.f32`
38×	`accelerator-lowering-fma.f64`
36×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	248
1	17	248
2	32	248
3	36	248
4	40	248
5	52	248
6	64	248
7	75	248
8	95	248
9	100	248
0	100	248

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

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

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

eval6.0ms (0.1%)

Memory: 12.5MiB live, 12.5MiB allocated
Compiler: Compiled 437 to 34 computations (92.2% saved)

prune3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	70	5	75

Accuracy

100.0%

Counts

75 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(fma.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))
✓	99.2%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
✓	100.0%	(hypot.f64 x x)
✓	51.9%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify4.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

cost-diff

(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))

✓

cost-diff

(fma.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))

✓

cost-diff

12288

(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
8×	`accelerator-lowering-fma.f32`
8×	`accelerator-lowering-fma.f64`
6×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	11	16
2	19	14
3	21	14
0	21	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
0
(+ (* x (pow (pow 2 1/4) 2)) 0)
x
(pow (pow 2 1/4) 2)
(pow 2 1/4)
2
1/4
0

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

localize27.0ms (0.4%)

Memory

-0.5MiB live, 38.0MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

✓

accuracy

100.0%

(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))

✓

accuracy

99.2%

(fma.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 0 binary64))

✓

accuracy

98.4%

(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))

Samples

18.0ms

256×

valid

Compiler

Compiled 23 to 10 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow: 4.0ms (41.6% of total)

ival-pow2: 2.0ms (20.8% of total)

ival-add: 1.0ms (10.4% of total)

ival-mult: 1.0ms (10.4% of total)

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Counts

3 → 12

Calls

Call 1

Inputs
#<alt (pow (pow 2 1/4) 2)>
#<alt (+ (* x (pow (pow 2 1/4) 2)) 0)>
#<alt (pow 2 1/4)>

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))>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ (* x (pow (pow 2 1/4) 2)) 0)
0.0ms	x	@	inf	(+ (* x (pow (pow 2 1/4) 2)) 0)
0.0ms	x	@	-inf	(+ (* x (pow (pow 2 1/4) 2)) 0)

rewrite359.0ms (5.5%)

Memory

-12.7MiB live, 348.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 984×	`-lowering-.f32`
2 984×	`-lowering-.f64`
2 852×	`accelerator-lowering-fma.f32`
2 852×	`accelerator-lowering-fma.f64`
2 458×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	41	9
2	270	9
3	3365	9
0	8346	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 353

Calls

Call 1

Inputs
(pow (pow 2 1/4) 2)
(+ (* x (pow (pow 2 1/4) 2)) 0)
(pow 2 1/4)

Outputs
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 4 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 8 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/4 binary64)) (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 1 binary64)))
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(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) x))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) x) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 x x) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x x))
(.f64 (/.f64 x (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 x x) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)))
(.f64 (/.f64 (.f64 x x) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)) (/.f64 #s(literal 2 binary64) (sqrt.f64 (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) x) (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 2 binary64) x))
(.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 (.f64 x x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (/.f64 (.f64 x x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)))
(.f64 (/.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)) (/.f64 (*.f64 x x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (fma.f64 #s(literal 4 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64)))
(.f64 (.f64 x (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 0 binary64)) (fma.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (fma.f64 (.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 0 binary64)) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))) (/.f64 x (/.f64 #s(literal 1/2 binary64) (.f64 x x))))
(*.f64 (exp.f64 (log.f64 x)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/4 binary64))) (log.f64 #s(literal 2 binary64))))
(exp.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))) (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))))
(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(literal 4 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/16 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (log.f64 #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) #s(literal 1/8 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))

simplify5.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`
2×	`sqrt-lowering-sqrt.f64`
2×	`sqrt-lowering-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48
0	5	48

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

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))

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)))

eval41.0ms (0.6%)

Memory: -28.8MiB live, 86.1MiB allocated
Compiler: Compiled 5 949 to 672 computations (88.7% saved)

prune47.0ms (0.7%)

Memory

13.0MiB live, 94.8MiB allocated

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	358	7	365
Fresh	0	0	0
Picked	1	1	2
Done	2	1	3
Total	361	9	370

Accuracy

100.0%

Counts

370 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
▶	99.2%	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
	99.3%	(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x x))
▶	99.6%	(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
	99.4%	(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
▶	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	51.7%	(.f64 #s(literal 2 binary64) (/.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	51.9%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 165 to 106 computations (35.8% saved)

simplify362.0ms (5.5%)

Memory

19.1MiB live, 379.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	cost-diff	0	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	cost-diff	384	(/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	704	(/.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	cost-diff	-64	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	5056	(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x))

Rules

6 564×	`/-lowering-/.f32`
6 564×	`/-lowering-/.f64`
4 814×	`associate-/r*`
4 590×	`-lowering-.f32`
4 590×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	181
1	44	181
2	128	131
3	331	99
4	665	99
5	1838	99
6	2025	99
7	2144	99
8	2279	99
9	2475	99
10	2696	99
11	2961	99
12	3272	99
13	3633	99
14	4067	99
15	4382	99
16	4586	99
17	4648	99
18	4711	99
19	4773	99
20	5081	99
0	8878	99

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2)))) (* (sqrt (sqrt (sqrt 2))) x))
(* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2))))
(sqrt (sqrt 2))
(sqrt 2)
2
(sqrt (sqrt (sqrt 2)))
(* (sqrt (sqrt (sqrt 2))) x)
x
(* (sqrt 2) x)
(sqrt 2)
2
x
(* 2 (/ (* x x) (+ (* (sqrt 2) x) 0)))
2
(/ (* x x) (+ (* (sqrt 2) x) 0))
(* x x)
x
(+ (* (sqrt 2) x) 0)
(sqrt 2)
0
(* (+ (* 2 x) 0) (/ x (+ (* (sqrt 2) x) 0)))
(+ (* 2 x) 0)
2
x
0
(/ x (+ (* (sqrt 2) x) 0))
(+ (* (sqrt 2) x) 0)
(sqrt 2)
(/ 1 (/ 1 (+ (* (sqrt 2) x) 0)))
1
(/ 1 (+ (* (sqrt 2) x) 0))
(+ (* (sqrt 2) x) 0)
(sqrt 2)
2
x
0

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

localize86.0ms (1.3%)

Memory

-9.2MiB live, 147.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	accuracy	99.2%	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	accuracy	99.2%	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	accuracy	99.2%	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (/.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.2%	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))
✓	accuracy	51.6%	(/.f64 (*.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	accuracy	100.0%	(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x)
✓	accuracy	99.7%	(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x))

Samples

38.0ms

256×

valid

Compiler

Compiled 143 to 23 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 10.0ms (41.8% of total)

ival-div: 6.0ms (25.1% of total)

ival-sqrt: 5.0ms (20.9% of total)

ival-add: 2.0ms (8.4% of total)

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

exact: 0.0ms (0% of total)

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

series76.0ms (1.2%)

Memory

7.1MiB live, 87.1MiB allocated

Counts

15 → 144

Calls

Call 1

Inputs
#<alt (* (* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2)))) (* (sqrt (sqrt (sqrt 2))) x))>
#<alt (* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2))))>
#<alt (sqrt (sqrt 2))>
#<alt (sqrt 2)>
#<alt (* (sqrt 2) x)>
#<alt (/ (* x x) (+ (* (sqrt 2) x) 0))>
#<alt (* x x)>
#<alt (+ (* (sqrt 2) x) 0)>
#<alt (/ x (+ (* (sqrt 2) x) 0))>
#<alt (* (+ (* 2 x) 0) (/ x (+ (* (sqrt 2) x) 0)))>
#<alt (+ (* 2 x) 0)>
#<alt (/ 1 (/ 1 (+ (* (sqrt 2) x) 0)))>
#<alt (/ 1 (+ (* (sqrt 2) x) 0))>
#<alt (* (sqrt (sqrt (sqrt 2))) x)>
#<alt (* 2 (/ (* x x) (+ (* (sqrt 2) x) 0)))>

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

Calls

36 calls:

Time	Variable		Point	Expression
68.0ms	x	@	0	(* (sqrt (sqrt (sqrt 2))) x)
2.0ms	x	@	-inf	(/ 1 (+ (* (sqrt 2) x) 0))
1.0ms	x	@	0	(/ (* x x) (+ (* (sqrt 2) x) 0))
1.0ms	x	@	0	(* (* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2)))) (* (sqrt (sqrt (sqrt 2))) x))
0.0ms	x	@	-inf	(* (+ (* 2 x) 0) (/ x (+ (* (sqrt 2) x) 0)))

rewrite555.0ms (8.5%)

Memory

3.1MiB live, 1 109.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 340×	`accelerator-lowering-fma.f32`
5 340×	`accelerator-lowering-fma.f64`
5 112×	`-lowering-.f32`
5 112×	`-lowering-.f64`
3 124×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	128
1	102	66
2	948	55
0	8595	55

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 3 922

Calls

Call 1

Inputs
(* (* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2)))) (* (sqrt (sqrt (sqrt 2))) x))
(* (sqrt (sqrt 2)) (sqrt (sqrt (sqrt 2))))
(sqrt (sqrt 2))
(sqrt 2)
(* (sqrt 2) x)
(/ (* x x) (+ (* (sqrt 2) x) 0))
(* x x)
(+ (* (sqrt 2) x) 0)
(/ x (+ (* (sqrt 2) x) 0))
(* (+ (* 2 x) 0) (/ x (+ (* (sqrt 2) x) 0)))
(+ (* 2 x) 0)
(/ 1 (/ 1 (+ (* (sqrt 2) x) 0)))
(/ 1 (+ (* (sqrt 2) x) 0))
(* (sqrt (sqrt (sqrt 2))) x)
(* 2 (/ (* x x) (+ (* (sqrt 2) x) 0)))

Outputs
(+.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
(+.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 0 binary64))
(exp.f64 (log.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(exp.f64 (*.f64 (log.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(-.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (/.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 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 (sqrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 x (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (.f64 (sqrt.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x) (/.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (pow.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 (*.f64 x x) #s(literal -4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 2 binary64)) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 x (fma.f64 (*.f64 x x) #s(literal -4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 x (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 0 binary64))
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(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) (*.f64 x x))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))) x)) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64))) (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)) (fma.f64 (*.f64 x x) #s(literal -2 binary64) #s(literal 0 binary64)) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 0 binary64))) (fma.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (*.f64 x x) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (fma.f64 #s(literal 2 binary64) (.f64 x x) #s(literal 0 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 x x) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64))) (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 #s(literal 64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 0 binary64))) (fma.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 16 binary64) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)) (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 8 binary64) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 16 binary64) #s(literal 0 binary64))) (fma.f64 x (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64) #s(literal 0 binary64))) (fma.f64 (*.f64 x x) #s(literal -4 binary64) #s(literal 0 binary64)))
(.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (*.f64 x x) #s(literal -4 binary64) #s(literal 0 binary64))) (fma.f64 x #s(literal -2 binary64) #s(literal 0 binary64)))

simplify53.0ms (0.8%)

Memory

-11.6MiB live, 145.2MiB allocated

Algorithm

1×	egg-herbie

Rules

90×	`-lowering-.f32`
90×	`-lowering-.f64`
42×	`/-lowering-/.f32`
42×	`/-lowering-/.f64`
26×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	648
1	27	648
2	51	648
3	54	648
4	81	648
5	101	648
6	112	648
0	112	648

Stop Event

1×	iter limit
1×	saturated

Counts

144 → 144

Calls

Call 1

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

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

eval1.3s (19.6%)

Memory: 88.4MiB live, 1 621.1MiB allocated
Compiler: Compiled 135 463 to 9 970 computations (92.6% saved)

prune724.0ms (11%)

Memory

-38.9MiB live, 1 468.1MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	6 302	4	6 306
Fresh	2	0	2
Picked	4	1	5
Done	0	2	2
Total	6 308	7	6 315

Accuracy

100.0%

Counts

6 315 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
	99.4%	(/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
	99.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
	99.3%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
✓	99.2%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	51.9%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 173 to 78 computations (54.9% saved)

regimes23.0ms (0.3%)

Memory

10.9MiB live, 49.4MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 2 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (/.f64 x (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) x #s(literal 0 binary64))))
(*.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x x))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(hypot.f64 x x)
(fma.f64 x (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 0 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	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
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)))

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)

regimes20.0ms (0.3%)

Memory

15.5MiB live, 53.5MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(+.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
99.6%	1	`x`
99.6%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.6%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.6%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes19.0ms (0.3%)

Memory

-13.3MiB live, 29.3MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	(pow.f64 x #s(literal 2 binary64))
4.0ms	x
4.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
4.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes25.0ms (0.4%)

Memory

-23.4MiB live, 14.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.3%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.3%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes9.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.2%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.2%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes5.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB 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
3.8%	1	`x`
3.8%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.8%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.8%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

simplify7.0ms (0.1%)

Memory

10.6MiB live, 10.6MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	20	35

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.0s (29.9%)

Memory

-12.2MiB live, 504.3MiB allocated

Rules

5 340×	`accelerator-lowering-fma.f32`
5 340×	`accelerator-lowering-fma.f64`
5 112×	`-lowering-.f32`
5 112×	`-lowering-.f64`
3 124×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (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	8	11
1	41	9
2	270	9
3	3365	9
0	8346	9
0	12	32
1	52	7
2	418	7
0	4043	7
0	5	14
1	25	10
0	167	9
0	21	128
1	102	66
2	948	55
0	8595	55

Stop Event

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

Compiler

Compiled 119 to 80 computations (32.8% saved)

preprocess47.0ms (0.7%)

Memory: -15.1MiB live, 105.6MiB allocated
Remove: (abs x)
Compiler: Compiled 122 to 56 computations (54.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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	9	248
1	17	248
2	32	248
3	36	248
4	40	248
5	52	248
6	64	248
7	75	248
8	95	248
9	100	248
0	100	248

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	9	248
1	17	248
2	32	248
3	36	248
4	40	248
5	52	248
6	64	248
7	75	248
8	95	248
9	100	248
0	100	248

analyze0.0ms (0%)

sample518.0ms (7.9%)

preprocess19.0ms (0.3%)

explain67.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize21.0ms (0.3%)

series3.0ms (0%)

rewrite38.0ms (0.6%)

simplify13.0ms (0.2%)

eval8.0ms (0.1%)

prune6.0ms (0.1%)

simplify6.0ms (0.1%)

localize34.0ms (0.5%)

series2.0ms (0%)

rewrite55.0ms (0.8%)

simplify14.0ms (0.2%)

eval6.0ms (0.1%)

prune3.0ms (0.1%)

simplify4.0ms (0.1%)

localize27.0ms (0.4%)

series0.0ms (0%)

rewrite359.0ms (5.5%)

simplify5.0ms (0.1%)

eval41.0ms (0.6%)

prune47.0ms (0.7%)

simplify362.0ms (5.5%)

localize86.0ms (1.3%)

series76.0ms (1.2%)

rewrite555.0ms (8.5%)

simplify53.0ms (0.8%)

eval1.3s (19.6%)

prune724.0ms (11%)

regimes23.0ms (0.3%)

regimes20.0ms (0.3%)

regimes19.0ms (0.3%)

regimes25.0ms (0.4%)

regimes9.0ms (0.1%)

regimes5.0ms (0.1%)

simplify7.0ms (0.1%)

soundness2.0s (29.9%)

preprocess47.0ms (0.7%)

end0.0ms (0%)

Profiling

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	9	248
1	17	248
2	32	248
3	36	248
4	40	248
5	52	248
6	64	248
7	75	248
8	95	248
9	100	248
0	100	248