Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample408.0ms (8.9%)

Memory

-6.9MiB live, 748.3MiB allocated

Samples

280.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-hypot: 135.0ms (94.6% of total)

ival-true: 5.0ms (3.5% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

preprocess17.0ms (0.4%)

Memory

-7.1MiB live, 30.2MiB allocated

Algorithm

2×	egg-herbie

Rules

40×	`associate-r`
34×	`sub-neg`
28×	`distribute-lft-neg-in`
24×	`neg-sub0`
22×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	25	19
2	68	19
3	166	19
4	243	19
5	254	19
6	256	19
0	4	6
1	8	6
2	11	6
3	14	6
0	14	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (* x x)))

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

Call 2

Inputs
(sqrt (+ (* x x) (* x x)))
(sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x))))
(neg (sqrt (+ (* (neg x) (neg x)) (* (neg x) (neg x)))))

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

Symmetry

(abs x)

explain74.0ms (1.6%)

Memory

3.2MiB live, 157.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
132	-	4	(1.7328238130188112e-162)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 x x))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	oflow-rescue	73	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	73
↳	`(*.f64 x x)`	overflow	146
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	55	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	55
↳	`(*.f64 x x)`	underflow	110

Confusion

	Predicted +	Predicted -
+	128	4
-	0	124

Precision

1.0

Recall

0.9696969696969697

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	4
-	0	0	124

Precision?

1.0

Recall?

0.9696969696969697

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 60 to 20 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-hypot: 14.0ms (70.9% of total)

ival-mult: 3.0ms (15.2% of total)

ival-add: 2.0ms (10.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.5%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify3.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	cost-diff	320	(+.f64 (.f64 x x) (.f64 x x))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
4×	`+-lowering-+.f64`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	15
1	8	15
2	11	15
3	14	15
0	14	12

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* x x) (* x x)))
(+ (* x x) (* x x))
(* x x)
x

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

localize19.0ms (0.4%)

Memory

7.1MiB live, 46.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 x x))
✓	accuracy	52.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

13.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-hypot: 4.0ms (58.5% of total)

ival-mult: 2.0ms (29.2% of total)

ival-add: 1.0ms (14.6% of total)

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

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

series3.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

3 → 36

Calls

Call 1

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

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

Calls

9 calls:

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

rewrite62.0ms (1.4%)

Memory

-10.1MiB live, 69.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

66×	`-lowering-.f32`
66×	`-lowering-.f64`
42×	`accelerator-lowering-fma.f32`
42×	`accelerator-lowering-fma.f64`
34×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	14
1	20	10
0	157	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

Inputs
(+ (* x x) (* x x))
(sqrt (+ (* x x) (* x x)))
(* x x)

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

simplify29.0ms (0.6%)

Memory

-17.3MiB live, 22.0MiB 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
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* 2 (pow x 2))
(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 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))

eval8.0ms (0.2%)

Memory: 21.9MiB live, 21.9MiB allocated
Compiler: Compiled 766 to 101 computations (86.8% saved)

prune7.0ms (0.1%)

Memory

-19.8MiB live, 19.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Accuracy

100.0%

Counts

86 → 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)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	52.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Compiler

Compiled 25 to 16 computations (36% saved)

simplify4.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB 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	5312	(hypot.f64 x x)
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(*.f64 (+.f64 x x) x)
✓	cost-diff	0	(sqrt.f64 (*.f64 (+.f64 x x) x))

Rules

22×	`-lowering-.f32`
22×	`-lowering-.f64`
10×	`*-commutative`
8×	`sqrt-lowering-sqrt.f64`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	21	48
2	25	48
0	25	42

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize45.0ms (1%)

Memory

-13.3MiB live, 105.2MiB 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	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 (+.f64 x x) x)
✓	accuracy	52.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Samples

28.0ms

256×

valid

Compiler

Compiled 48 to 15 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sqrt: 6.0ms (32.3% of total)

ival-add: 4.0ms (21.5% of total)

ival-mult: 4.0ms (21.5% of total)

ival-hypot: 4.0ms (21.5% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

9 → 96

Calls

Call 1

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

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

24 calls:

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

rewrite56.0ms (1.2%)

Memory

2.9MiB live, 77.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

772×	`frac-times`
348×	`times-frac`
296×	`-lowering-.f32`
296×	`-lowering-.f64`
182×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	46
1	56	11
2	424	11
0	3854	11

Stop Event

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

Counts

9 → 21

Calls

Call 1

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

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

simplify201.0ms (4.4%)

Memory

-24.2MiB live, 110.9MiB allocated

Algorithm

1×	egg-herbie

Rules

1 478×	`associate-r`
1 232×	`-lowering-.f32`
1 232×	`-lowering-.f64`
1 232×	`accelerator-lowering-fma.f32`
1 232×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	412
1	50	412
2	136	412
3	265	412
4	490	412
5	809	412
6	1411	412
7	1537	412
8	1592	412
9	1630	412
10	1808	412
11	2022	412
12	2068	412
13	2096	412
14	2100	412
15	2100	412
16	2246	412
17	2430	412
18	3585	412
19	3703	412
20	3727	412
21	3735	412
22	3739	412
23	3743	412
24	3855	412
25	3903	412
26	3903	412
27	4085	412
0	4085	412

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

eval11.0ms (0.2%)

Memory: 22.6MiB live, 22.6MiB allocated
Compiler: Compiled 911 to 71 computations (92.2% saved)

prune30.0ms (0.7%)

Memory

-27.6MiB live, 12.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	128	6	134

Accuracy

100.0%

Counts

134 → 6

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)
▶	99.0%	(*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	52.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	3.6%	#s(literal 0 binary64)

Compiler

Compiled 37 to 25 computations (32.4% saved)

simplify4.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1600	(*.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)) #s(literal 0 binary64)))

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
12×	`accelerator-lowering-fma.f32`
12×	`accelerator-lowering-fma.f64`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	18	21
2	24	17
3	25	17
4	26	17
0	26	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize29.0ms (0.6%)

Memory

19.8MiB live, 59.7MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

16.0ms

256×

valid

Compiler

Compiled 25 to 10 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (38.9% of total)

ival-sqrt: 3.0ms (38.9% of total)

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

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

4 → 36

Calls

Call 1

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

Calls

9 calls:

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

rewrite270.0ms (5.9%)

Memory

-28.1MiB live, 505.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 086×	`accelerator-lowering-fma.f32`
3 086×	`accelerator-lowering-fma.f64`
2 782×	`-lowering-.f32`
2 782×	`-lowering-.f64`
1 596×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	35	14
2	282	12
3	3522	12
0	8448	12

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 410

Calls

Call 1

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

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

simplify40.0ms (0.9%)

Memory

-8.2MiB live, 69.1MiB allocated

Algorithm

1×	egg-herbie

Rules

464×	`-lowering-.f32`
464×	`-lowering-.f64`
464×	`accelerator-lowering-fma.f32`
464×	`accelerator-lowering-fma.f64`
312×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	132
1	37	132
2	134	132
3	266	132
4	677	132
5	884	132
6	1014	132
7	1043	132
8	1045	132
9	1045	132
0	1045	132

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

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

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

eval56.0ms (1.2%)

Memory: 25.7MiB live, 104.2MiB allocated
Compiler: Compiled 7 738 to 952 computations (87.7% saved)

prune57.0ms (1.3%)

Memory

-0.7MiB live, 117.3MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	470	4	474
Fresh	0	0	0
Picked	1	1	2
Done	2	2	4
Total	473	7	480

Accuracy

100.0%

Counts

480 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
▶	99.0%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	99.3%	(.f64 (sqrt.f64 x) (.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify21.0ms (0.5%)

Memory

-11.7MiB live, 26.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
✓	cost-diff	0	(/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	320	(*.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	1600	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Rules

300×	`-lowering-.f32`
300×	`-lowering-.f64`
190×	`associate-r`
168×	`associate-l`
108×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	81
1	37	81
2	71	81
3	175	81
4	328	81
5	368	81
6	402	81
7	402	81
8	414	81
9	433	81
10	442	81
11	449	81
12	455	81
0	455	81

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize63.0ms (1.4%)

Memory

-14.7MiB live, 143.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
✓	accuracy	100.0%	(*.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(/.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.3%	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.5%	(.f64 x (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x))))
✓	accuracy	99.5%	(.f64 (sqrt.f64 x) (.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1/2 binary64) x)))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Samples

38.0ms

256×

valid

Compiler

Compiled 92 to 21 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-mult: 11.0ms (42.7% of total)

ival-sqrt: 8.0ms (31% of total)

ival-div: 5.0ms (19.4% of total)

ival-add: 1.0ms (3.9% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

13 → 144

Calls

Call 1

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

Calls

36 calls:

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

rewrite465.0ms (10.2%)

Memory

36.0MiB live, 902.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 882×	`accelerator-lowering-fma.f32`
3 882×	`accelerator-lowering-fma.f64`
3 508×	`-lowering-.f32`
3 508×	`-lowering-.f64`
2 064×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	75	48
2	480	48
3	4474	48
0	8617	48

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 3 312

Calls

Call 1

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

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

simplify197.0ms (4.3%)

Memory

-6.3MiB live, 307.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2 880×	`-lowering-.f32`
2 880×	`-lowering-.f64`
1 884×	`/-lowering-/.f32`
1 884×	`/-lowering-/.f64`
1 850×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	792
1	93	792
2	261	792
3	471	792
4	1396	792
5	3394	792
6	6175	792
7	7870	792
0	8137	792

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval667.0ms (14.6%)

Memory: -254.4MiB live, 684.7MiB allocated
Compiler: Compiled 64 802 to 4 408 computations (93.2% saved)

prune219.0ms (4.8%)

Memory

2.4MiB live, 407.8MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	3 596	2	3 598
Fresh	0	0	0
Picked	3	1	4
Done	0	3	3
Total	3 599	6	3 605

Accuracy

100.0%

Counts

3 605 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.2%	(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
	99.3%	(/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	52.6%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	3.6%	#s(literal 0 binary64)

Compiler

Compiled 124 to 61 computations (50.8% saved)

regimes25.0ms (0.5%)

Memory

-19.8MiB live, 19.0MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

12.0ms	(*.f64 x x)
4.0ms	x
4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes16.0ms (0.3%)

Memory

17.9MiB live, 17.9MiB allocated

Counts

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes15.0ms (0.3%)

Memory

-22.8MiB live, 17.1MiB allocated

Counts

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

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

Calls

4 calls:

7.0ms	(+.f64 (.f64 x x) (.f64 x x))
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes9.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes6.0ms (0.1%)

Memory

-27.1MiB live, 11.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

2.0ms	x
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))
1.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify7.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	16	21

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.3s (29.4%)

Memory

6.7MiB live, 396.9MiB allocated

Rules

3 882×	`accelerator-lowering-fma.f32`
3 882×	`accelerator-lowering-fma.f64`
3 508×	`-lowering-.f32`
3 508×	`-lowering-.f64`
3 086×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	412
1	50	412
2	136	412
3	265	412
4	490	412
5	809	412
6	1411	412
7	1537	412
8	1592	412
9	1630	412
10	1808	412
11	2022	412
12	2068	412
13	2096	412
14	2100	412
15	2100	412
16	2246	412
17	2430	412
18	3585	412
19	3703	412
20	3727	412
21	3735	412
22	3739	412
23	3743	412
24	3855	412
25	3903	412
26	3903	412
27	4085	412
0	4085	412
0	8	15
1	35	14
2	282	12
3	3522	12
0	8448	12
0	4	14
1	20	10
0	157	9
0	19	48
1	75	48
2	480	48
3	4474	48
0	8617	48
0	15	46
1	56	11
2	424	11
0	3854	11

Stop Event

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

Compiler

Compiled 72 to 47 computations (34.7% saved)

preprocess71.0ms (1.6%)

Memory: -5.7MiB live, 78.5MiB allocated
Remove: (abs x)
Compiler: Compiled 78 to 42 computations (46.2% 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	19	81
1	37	81
2	71	81
3	175	81
4	328	81
5	368	81
6	402	81
7	402	81
8	414	81
9	433	81
10	442	81
11	449	81
12	455	81
0	455	81

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	19	81
1	37	81
2	71	81
3	175	81
4	328	81
5	368	81
6	402	81
7	402	81
8	414	81
9	433	81
10	442	81
11	449	81
12	455	81
0	455	81

analyze0.0ms (0%)

sample408.0ms (8.9%)

preprocess17.0ms (0.4%)

explain74.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize19.0ms (0.4%)

series3.0ms (0.1%)

rewrite62.0ms (1.4%)

simplify29.0ms (0.6%)

eval8.0ms (0.2%)

prune7.0ms (0.1%)

simplify4.0ms (0.1%)

localize45.0ms (1%)

series5.0ms (0.1%)

rewrite56.0ms (1.2%)

simplify201.0ms (4.4%)

eval11.0ms (0.2%)

prune30.0ms (0.7%)

simplify4.0ms (0.1%)

localize29.0ms (0.6%)

series2.0ms (0%)

rewrite270.0ms (5.9%)

simplify40.0ms (0.9%)

eval56.0ms (1.2%)

prune57.0ms (1.3%)

simplify21.0ms (0.5%)

localize63.0ms (1.4%)

series9.0ms (0.2%)

rewrite465.0ms (10.2%)

simplify197.0ms (4.3%)

eval667.0ms (14.6%)

prune219.0ms (4.8%)

regimes25.0ms (0.5%)

regimes16.0ms (0.3%)

regimes15.0ms (0.3%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

simplify7.0ms (0.1%)

soundness1.3s (29.4%)

preprocess71.0ms (1.6%)

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	19	81
1	37	81
2	71	81
3	175	81
4	328	81
5	368	81
6	402	81
7	402	81
8	414	81
9	433	81
10	442	81
11	449	81
12	455	81
0	455	81