Metrics for sqrt E (should all be same)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample521.0ms (12%)

Memory

8.0MiB live, 707.6MiB allocated

Samples

365.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 193.0ms

ival-pow2: 85.0ms (44% of total)

ival-sqrt: 66.0ms (34.2% of total)

ival-add: 35.0ms (18.1% of total)

ival-true: 5.0ms (2.6% of total)

ival-assert: 2.0ms (1% of total)

Bogosity

preprocess19.0ms (0.4%)

Memory

-8.1MiB live, 30.6MiB 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)

explain66.0ms (1.5%)

Memory

33.9MiB live, 111.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
119	-	1	(1.9637629074315958e-162)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	60	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	60
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	120
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	58	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	58
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	116

Confusion

	Predicted +	Predicted -
+	118	1
-	0	137

Precision

1.0

Recall

0.9915966386554622

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	118	0	1
-	0	0	137

Precision?

1.0

Recall?

0.9915966386554622

Freqs

test

number	freq
0	138
1	118

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: 13.0ms

ival-pow2: 7.0ms (52.5% of total)

ival-sqrt: 3.0ms (22.5% of total)

ival-add: 2.0ms (15% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.7%	(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)

simplify7.0ms (0.2%)

Memory

-39.1MiB live, 4.9MiB 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)

localize18.0ms (0.4%)

Memory

26.9MiB live, 26.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	accuracy	56.7%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

11.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-pow2: 3.0ms (51.1% of total)

ival-sqrt: 2.0ms (34.1% of total)

ival-add: 1.0ms (17% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.9MiB 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))

rewrite43.0ms (1%)

Memory

-25.0MiB live, 50.7MiB 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)))

simplify9.0ms (0.2%)

Memory

14.0MiB live, 14.0MiB 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 (0.2%)

Memory: 15.5MiB live, 15.5MiB allocated
Compiler: Compiled 790 to 110 computations (86.1% saved)

prune8.0ms (0.2%)

Memory

-24.8MiB live, 13.4MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Accuracy

100.0%

Counts

88 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
▶	100.0%	(hypot.f64 x x)
▶	15.1%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))))
▶	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 44 to 22 computations (50% saved)

simplify1.1s (24.6%)

Memory

31.3MiB live, 1 263.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 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	5248	(hypot.f64 x x)
✓	cost-diff	0	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))))
✓	cost-diff	1216	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))))
✓	cost-diff	2880	(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	cost-diff	-64	(*.f64 x (+.f64 x x))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (*.f64 x (+.f64 x x)))

Rules

48 726×	`accelerator-lowering-fma.f32`
48 726×	`accelerator-lowering-fma.f64`
5 896×	`-lowering-.f32`
5 896×	`-lowering-.f64`
3 386×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	97
1	38	77
2	182	71
3	1007	69
4	2984	69
5	3400	69
6	4028	69
7	5083	69
8	5999	69
9	6328	69
0	8393	60

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize113.0ms (2.6%)

Memory

-27.1MiB live, 89.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
✓	accuracy	100.0%	(hypot.f64 x x)
✓	accuracy	99.8%	(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x)))))
✓	accuracy	56.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))))
✓	accuracy	21.7%	(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 x (+.f64 x x))
✓	accuracy	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Samples

63.0ms

256×

valid

Compiler

Compiled 141 to 20 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 36.0ms (68.4% of total)

ival-sqrt: 5.0ms (9.5% of total)

ival-add: 4.0ms (7.6% of total)

ival-hypot: 4.0ms (7.6% of total)

ival-div: 3.0ms (5.7% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Counts

10 → 108

Calls

Call 1

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

27 calls:

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

rewrite176.0ms (4.1%)

Memory

-2.4MiB live, 355.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 952×	`accelerator-lowering-fma.f32`
2 952×	`accelerator-lowering-fma.f64`
2 034×	`-lowering-.f32`
2 034×	`-lowering-.f64`
1 164×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	108	13
2	1227	13
3	6558	13
0	8315	13

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 234

Calls

Call 1

Inputs
(sqrt (* x (+ x x)))
(+ x x)
(* x (+ x x))
(/ (+ (* (* x x) (* x x)) 0) (* (+ (* (* x x) (* x x)) 0) (* x (+ x x))))
(/ 1 (/ (+ (* (* x x) (* x x)) 0) (* (+ (* (* x x) (* x x)) 0) (* x (+ x x)))))
(sqrt (/ 1 (/ (+ (* (* x x) (* x x)) 0) (* (+ (* (* x x) (* x x)) 0) (* x (+ x x))))))
(+ (* (* x x) (* x x)) 0)
(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)
#s(literal 0 binary64)
(+.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(exp.f64 (fma.f64 #s(literal 4 binary64) (log.f64 x) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (*.f64 (fma.f64 #s(literal 4 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (fma.f64 #s(literal -4 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (fma.f64 #s(literal 8 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal -2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 4 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (fma.f64 #s(literal 4 binary64) (log.f64 x) #s(literal 0 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(-.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(fma.f64 x (*.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 x (/.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 x (*.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (/.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 x (fma.f64 x x #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 1 binary64)) #s(literal 0 binary64))
(fma.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) x #s(literal 0 binary64))
(fma.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) (/.f64 (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) (/.f64 x #s(literal 1 binary64)) #s(literal 0 binary64))
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(.f64 (/.f64 (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (*.f64 x (fma.f64 x x #s(literal 0 binary64))) (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) (*.f64 x (fma.f64 x x #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64))) x) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))))
(.f64 (/.f64 (fma.f64 x (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (*.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))))
(.f64 (/.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))) (/.f64 (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))))
(.f64 (/.f64 (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))) (/.f64 (.f64 x (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))))
(.f64 (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (*.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64))) (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))))
(.f64 (/.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 x (*.f64 x (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) #s(literal 0 binary64)) (pow.f64 x #s(literal 24 binary64))) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))
(*.f64 (/.f64 (fma.f64 (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64))))
(.f64 (.f64 x (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
#s(literal 0 binary64)
#s(literal 0 binary64)
(exp.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 4 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #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)))

simplify18.0ms (0.4%)

Memory

7.1MiB live, 45.1MiB 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	13	456
1	21	456
2	38	456
3	42	456
4	46	456
5	58	456
6	70	456
7	81	456
8	101	456
9	106	456
0	106	456

Stop Event

1×	iter limit
1×	saturated

Counts

108 → 108

Calls

Call 1

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

eval66.0ms (1.5%)

Memory: 41.9MiB live, 149.4MiB allocated
Compiler: Compiled 25 540 to 1 920 computations (92.5% saved)

prune60.0ms (1.4%)

Memory

-3.1MiB live, 157.6MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	593	2	595
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	594	5	599

Accuracy

100.0%

Counts

599 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(fma.f64 x (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
✓	100.0%	(hypot.f64 x x)
▶	56.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))))
✓	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	3.8%	#s(literal 0 binary64)

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify6.0ms (0.1%)

Memory

-29.8MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))))
✓	cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64))))

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
20×	`/-lowering-/.f32`
20×	`/-lowering-/.f64`
18×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	15	24
2	27	24
3	32	24
4	34	24
5	40	24
6	61	24
0	61	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize26.0ms (0.6%)

Memory

20.7MiB live, 60.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x #s(literal 0 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64))))
✓	accuracy	99.1%	(/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))
✓	accuracy	56.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))))

Samples

16.0ms

256×

valid

Compiler

Compiled 34 to 11 computations (67.6% saved)

Precisions

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

ival-div: 3.0ms (34.8% of total)

ival-mult: 2.0ms (23.2% of total)

ival-sqrt: 2.0ms (23.2% of total)

ival-add: 1.0ms (11.6% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite188.0ms (4.3%)

Memory

5.2MiB live, 289.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 620×	`-lowering-.f32`
1 620×	`-lowering-.f64`
1 534×	`/-lowering-/.f32`
1 534×	`/-lowering-/.f64`
1 430×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	53	19
2	384	17
0	3725	17

Stop Event

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

Counts

4 → 694

Calls

Call 1

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

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

simplify25.0ms (0.6%)

Memory

-18.0MiB live, 26.8MiB 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	10	208
1	17	208
2	36	208
3	41	208
4	45	208
5	57	208
6	69	208
7	80	208
8	100	208
9	105	208
0	105	208

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

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

eval141.0ms (3.3%)

Memory: 4.7MiB live, 154.4MiB allocated
Compiler: Compiled 19 276 to 2 266 computations (88.2% saved)

prune82.0ms (1.9%)

Memory

9.4MiB live, 208.4MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	738	4	742
Fresh	0	0	0
Picked	1	1	2
Done	2	1	3
Total	741	6	747

Accuracy

100.0%

Counts

747 → 6

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))
▶	99.3%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	99.2%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 34 to 26 computations (23.5% saved)

simplify5.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	1088	(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Rules

20×	`-lowering-.f32`
20×	`-lowering-.f64`
16×	`/-lowering-/.f32`
16×	`/-lowering-/.f64`
8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	21	46
2	22	46
3	29	46
4	29	46
5	32	46
6	35	46
0	35	46

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize204.0ms (4.7%)

Memory

-50.1MiB live, 98.8MiB allocated

Localize:

Found 11 expressions of interest:

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

Samples

188.0ms

256×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-sqrt: 168.0ms (94.4% of total)

ival-div: 5.0ms (2.8% of total)

ival-mult: 4.0ms (2.2% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

10 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite259.0ms (6%)

Memory

1.0MiB live, 388.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 562×	`-lowering-.f32`
2 562×	`-lowering-.f64`
1 500×	`+-lowering-+.f64`
1 500×	`+-lowering-+.f32`
1 498×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	49	32
2	180	32
3	1000	32
4	6804	32
0	8605	32

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 1 256

Calls

Call 1

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

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

simplify243.0ms (5.6%)

Memory

17.9MiB live, 204.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 232×	`-lowering-.f32`
1 232×	`-lowering-.f64`
1 232×	`accelerator-lowering-fma.f32`
1 232×	`accelerator-lowering-fma.f64`
950×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	380
1	49	380
2	121	380
3	247	380
4	485	380
5	797	380
6	1301	380
7	1420	380
8	1472	380
9	1526	380
10	1701	380
11	1950	380
12	2034	380
13	2138	380
14	2172	380
15	2236	380
16	2408	380
17	2440	380
18	2456	380
19	2456	380
20	2535	380
21	2751	380
22	3819	380
23	4035	380
24	4137	380
25	4211	380
26	4223	380
27	4255	380
28	4459	380
29	4523	380
30	4523	380
31	4523	380
32	4642	380
0	4642	380

Stop Event

1×	iter limit
1×	saturated

Counts

96 → 96

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

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

eval225.0ms (5.2%)

Memory: 27.6MiB live, 340.7MiB allocated
Compiler: Compiled 16 318 to 1 496 computations (90.8% saved)

prune124.0ms (2.9%)

Memory

-25.0MiB live, 175.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	1 420	0	1 420
Fresh	0	0	0
Picked	0	4	4
Done	0	2	2
Total	1 420	6	1 426

Accuracy

100.0%

Counts

1 426 → 6

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))
✓	99.3%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	99.2%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	3.8%	#s(literal 0 binary64)

Compiler

Compiled 114 to 59 computations (48.2% saved)

regimes15.0ms (0.4%)

Memory

22.8MiB live, 22.8MiB allocated

Counts

11 → 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 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal 0 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64)) (.f64 x (+.f64 x x))))))
(hypot.f64 x x)
(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:

4.0ms	x
4.0ms	(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))))
3.0ms	(+.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)

regimes4.0ms (0.1%)

Memory

7.6MiB live, 7.5MiB allocated

Counts

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Memory

-34.9MiB live, 3.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
3.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Memory

13.5MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness526.0ms (12.2%)

Memory

-6.2MiB live, 207.9MiB allocated

Rules

2 952×	`accelerator-lowering-fma.f32`
2 952×	`accelerator-lowering-fma.f64`
2 034×	`-lowering-.f32`
2 034×	`-lowering-.f64`
1 620×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	108	13
2	1227	13
3	6558	13
0	8315	13
0	9	19
1	53	19
2	384	17
0	3725	17
0	5	14
1	25	10
0	167	9
0	13	456
1	21	456
2	38	456
3	42	456
4	46	456
5	58	456
6	70	456
7	81	456
8	101	456
9	106	456
0	106	456

Stop Event

1×	done
1×	iter limit
1×	saturated
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

Compiler

Compiled 38 to 27 computations (28.9% saved)

preprocess32.0ms (0.7%)

Memory: -10.1MiB live, 69.3MiB allocated
Remove: (abs x)
Compiler: Compiled 52 to 30 computations (42.3% 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	13	456
1	21	456
2	38	456
3	42	456
4	46	456
5	58	456
6	70	456
7	81	456
8	101	456
9	106	456
0	106	456

Iter	Nodes	Cost
0	10	208
1	17	208
2	36	208
3	41	208
4	45	208
5	57	208
6	69	208
7	80	208
8	100	208
9	105	208
0	105	208

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	13	456
1	21	456
2	38	456
3	42	456
4	46	456
5	58	456
6	70	456
7	81	456
8	101	456
9	106	456
0	106	456

Iter	Nodes	Cost
0	10	208
1	17	208
2	36	208
3	41	208
4	45	208
5	57	208
6	69	208
7	80	208
8	100	208
9	105	208
0	105	208

analyze0.0ms (0%)

sample521.0ms (12%)

preprocess19.0ms (0.4%)

explain66.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.2%)

localize18.0ms (0.4%)

series3.0ms (0.1%)

rewrite43.0ms (1%)

simplify9.0ms (0.2%)

eval8.0ms (0.2%)

prune8.0ms (0.2%)

simplify1.1s (24.6%)

localize113.0ms (2.6%)

series4.0ms (0.1%)

rewrite176.0ms (4.1%)

simplify18.0ms (0.4%)

eval66.0ms (1.5%)

prune60.0ms (1.4%)

simplify6.0ms (0.1%)

localize26.0ms (0.6%)

series1.0ms (0%)

rewrite188.0ms (4.3%)

simplify25.0ms (0.6%)

eval141.0ms (3.3%)

prune82.0ms (1.9%)

simplify5.0ms (0.1%)

localize204.0ms (4.7%)

series6.0ms (0.1%)

rewrite259.0ms (6%)

simplify243.0ms (5.6%)

eval225.0ms (5.2%)

prune124.0ms (2.9%)

regimes15.0ms (0.4%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify7.0ms (0.2%)

soundness526.0ms (12.2%)

preprocess32.0ms (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	13	456
1	21	456
2	38	456
3	42	456
4	46	456
5	58	456
6	70	456
7	81	456
8	101	456
9	106	456
0	106	456

Iter	Nodes	Cost
0	10	208
1	17	208
2	36	208
3	41	208
4	45	208
5	57	208
6	69	208
7	80	208
8	100	208
9	105	208
0	105	208