Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 4 computations (60% saved)

sample419.0ms (2.9%)

Memory

14.4MiB live, 883.3MiB allocated

Samples

301.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-hypot: 159.0ms (94.2% of total)

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

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

Bogosity

preprocess17.0ms (0.1%)

Memory

-5.1MiB live, 33.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	21	13
2	66	13
3	166	13
4	247	13
5	256	13
6	258	13
0	4	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)))

Symmetry

(abs x)

explain70.0ms (0.5%)

Memory

-10.7MiB live, 117.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
127	-	1	(1.1434135325736018e-156)	`(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	76	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	overflow	76
↳	`(*.f64 x x)`	overflow	152
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`	uflow-rescue	50	0
↳	`(+.f64 (.f64 x x) (.f64 x x))`	underflow	50
↳	`(*.f64 x x)`	underflow	100

Confusion

	Predicted +	Predicted -
+	126	1
-	0	129

Precision

1.0

Recall

0.9921259842519685

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	126	0	1
-	0	0	129

Precision?

1.0

Recall?

0.9921259842519685

Freqs

test

number	freq
0	130
1	126

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 60 to 20 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 9.0ms (49.9% of total)

ival-mult: 6.0ms (33.3% of total)

ival-add: 2.0ms (11.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify3.0ms (0%)

Memory

4.4MiB live, 4.4MiB 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

localize23.0ms (0.2%)

Memory

-9.3MiB live, 29.8MiB 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	54.1%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Samples

17.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

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

ival-hypot: 4.0ms (55.5% of total)

ival-mult: 2.0ms (27.7% of total)

ival-add: 1.0ms (13.9% of total)

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

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

series3.0ms (0%)

Memory

4.3MiB live, 4.3MiB 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)))
0.0ms	x	@	0	(+ (* x x) (* x x))
0.0ms	x	@	inf	(+ (* x x) (* x x))
0.0ms	x	@	-inf	(+ (* x x) (* x x))

rewrite47.0ms (0.3%)

Memory

8.6MiB live, 47.4MiB 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)))

simplify11.0ms (0.1%)

Memory

-11.4MiB live, 26.7MiB 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))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* x (sqrt 2)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval8.0ms (0.1%)

Memory: 22.4MiB live, 22.3MiB allocated
Compiler: Compiled 702 to 94 computations (86.6% saved)

prune8.0ms (0.1%)

Memory

-27.2MiB live, 13.0MiB 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
▶	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	54.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

simplify4.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	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	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	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×	`sqrt-lowering-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	18	47
2	21	47
0	21	41

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize41.0ms (0.3%)

Memory

0.9MiB live, 76.5MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	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%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 (+.f64 x x) x)
✓	accuracy	54.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Samples

28.0ms

256×

valid

Compiler

Compiled 46 to 13 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sqrt: 6.0ms (35.6% of total)

ival-mult: 4.0ms (23.8% of total)

ival-hypot: 4.0ms (23.8% of total)

ival-add: 1.0ms (5.9% 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%)

Memory

10.3MiB live, 10.3MiB allocated

Counts

9 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite33.0ms (0.2%)

Memory

17.2MiB live, 52.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

98×	`-lowering-.f32`
98×	`-lowering-.f64`
68×	`accelerator-lowering-fma.f32`
68×	`accelerator-lowering-fma.f64`
58×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	41	30
0	243	26

Stop Event

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

Counts

9 → 126

Calls

Call 1

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

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

simplify176.0ms (1.2%)

Memory

-19.8MiB live, 176.1MiB 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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(sqrt x)
(sqrt 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)))

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

eval23.0ms (0.2%)

Memory: 25.4MiB live, 64.1MiB allocated
Compiler: Compiled 2 297 to 230 computations (90% saved)

prune17.0ms (0.1%)

Memory

-29.1MiB live, 48.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	258	6	264

Accuracy

100.0%

Counts

264 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	26.4%	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (fma.f64 x x #s(literal 0 binary64))))
▶	7.0%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))

Compiler

Compiled 46 to 26 computations (43.5% saved)

simplify359.0ms (2.5%)

Memory

4.0MiB live, 340.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (fma.f64 x x #s(literal 0 binary64))))
✓	cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	1664	(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (fma.f64 x x #s(literal 0 binary64)))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))

Rules

7 074×	`accelerator-lowering-fma.f32`
7 074×	`accelerator-lowering-fma.f64`
6 400×	`-lowering-.f32`
6 400×	`-lowering-.f64`
2 090×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	59
1	24	51
2	85	45
3	240	37
4	380	37
5	999	37
6	2053	37
7	2561	37
8	3493	37
9	4836	37
10	5216	37
11	5360	37
12	6676	37
13	6982	37
14	7106	37
0	8045	34

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize12.5s (85.9%)

Memory

-7.1MiB live, 34.4MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x)
✓	accuracy	54.1%	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (fma.f64 x x #s(literal 0 binary64))))
✓	accuracy	33.6%	(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (fma.f64 x x #s(literal 0 binary64)))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))

Samples

12.5s

256×

valid

Compiler

Compiled 68 to 12 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.5s

ival-mult: 12.5s (99.9% of total)

ival-add: 3.0ms (0% of total)

ival-sqrt: 3.0ms (0% of total)

ival-div: 2.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

7 → 84

Calls

Call 1

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

Outputs
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* (sqrt x) (sqrt 2))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>

Calls

21 calls:

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

rewrite62.0ms (0.4%)

Memory

28.9MiB live, 78.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

114×	`/-lowering-/.f32`
114×	`/-lowering-/.f64`
88×	`-lowering-.f32`
88×	`-lowering-.f64`
64×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	65	9
0	679	9

Stop Event

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

Counts

7 → 28

Calls

Call 1

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

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

simplify32.0ms (0.2%)

Memory

-3.7MiB live, 35.2MiB allocated

Algorithm

1×	egg-herbie

Rules

162×	`-lowering-.f32`
162×	`-lowering-.f64`
158×	`accelerator-lowering-fma.f32`
158×	`accelerator-lowering-fma.f64`
104×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	380
1	44	380
2	96	380
3	155	380
4	172	380
5	218	380
6	263	380
7	294	380
8	363	380
9	383	380
10	383	380
0	383	380

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

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

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

eval13.0ms (0.1%)

Memory: 22.1MiB live, 22.1MiB allocated
Compiler: Compiled 2 185 to 212 computations (90.3% saved)

prune26.0ms (0.2%)

Memory

-59.7MiB live, 18.6MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	158	7	165

Accuracy

100.0%

Counts

165 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	26.4%	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (*.f64 x x)))
✓	7.0%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	3.5%	#s(literal 0 binary64)

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify340.0ms (2.3%)

Memory

17.6MiB live, 447.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (*.f64 x x)))
✓	cost-diff	64	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	1664	(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (*.f64 x x))

Rules

6 778×	`-lowering-.f32`
6 778×	`-lowering-.f64`
5 432×	`accelerator-lowering-fma.f32`
5 432×	`accelerator-lowering-fma.f64`
2 302×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	55
1	29	43
2	95	33
3	262	33
4	629	33
5	2223	33
6	3362	33
7	3954	33
8	4920	33
9	6339	33
10	6759	33
11	6925	33
12	7055	33
13	7192	33
14	7338	33
0	8351	30

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize35.0ms (0.2%)

Memory

1.1MiB live, 79.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))
✓	accuracy	99.9%	(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x)
✓	accuracy	54.1%	(sqrt.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (*.f64 x x)))
✓	accuracy	33.6%	(/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x) (*.f64 x x))

Samples

23.0ms

256×

valid

Compiler

Compiled 62 to 11 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 9.0ms (60.5% of total)

ival-div: 2.0ms (13.4% of total)

ival-add: 2.0ms (13.4% of total)

ival-sqrt: 2.0ms (13.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x))>
#<alt (+ (* x x) 0)>
#<alt (sqrt (/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x)))>
#<alt (* (* (+ (* x x) 0) (+ x x)) x)>
#<alt (* (+ (* x x) 0) (+ 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 (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* x (sqrt 2))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* -1 (* x (sqrt 2)))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 4))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>
#<alt (* 2 (pow x 3))>

Calls

15 calls:

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

rewrite38.0ms (0.3%)

Memory

5.3MiB live, 81.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

110×	`/-lowering-/.f32`
110×	`/-lowering-/.f64`
88×	`-lowering-.f32`
88×	`-lowering-.f64`
64×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	55
1	63	7
0	710	7

Stop Event

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

Counts

5 → 26

Calls

Call 1

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

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

simplify16.0ms (0.1%)

Memory

-4.8MiB live, 35.4MiB allocated

Algorithm

1×	egg-herbie

Rules

58×	`-lowering-.f32`
58×	`-lowering-.f64`
54×	`accelerator-lowering-fma.f32`
54×	`accelerator-lowering-fma.f64`
44×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	268
1	25	268
2	48	268
3	59	268
4	63	268
5	75	268
6	87	268
7	98	268
8	126	268
9	138	268
0	138	268

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

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

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

eval7.0ms (0.1%)

Memory: 19.7MiB live, 19.7MiB allocated
Compiler: Compiled 1 094 to 152 computations (86.1% saved)

prune8.0ms (0.1%)

Memory

-17.2MiB live, 20.5MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	86	7	93

Accuracy

100.0%

Counts

93 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
	26.4%	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 x x) (+.f64 x x)) x) (.f64 x x)))
✓	7.0%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	3.5%	#s(literal 0 binary64)

Compiler

Compiled 125 to 53 computations (57.6% saved)

regimes16.0ms (0.1%)

Memory

-8.6MiB live, 29.3MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

5.0ms	x
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
3.0ms	(*.f64 x x)
3.0ms	(+.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)

regimes13.0ms (0.1%)

Memory

28.6MiB live, 28.6MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(+.f64 (.f64 x x) (.f64 x x))
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.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)

regimes11.0ms (0.1%)

Memory

-15.2MiB live, 22.4MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(+.f64 (.f64 x x) (.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%)

Memory

23.4MiB live, 23.4MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
7.0%	1	`x`
7.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
7.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
7.0%	1	`(*.f64 x x)`

Compiler

Compiled 23 to 10 computations (56.5% saved)

regimes20.0ms (0.1%)

Memory

-25.2MiB live, 19.6MiB 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:

16.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
3.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
3.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
3.5%	1	`(*.f64 x x)`
3.5%	1	`x`

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify7.0ms (0%)

Memory

16.3MiB live, 16.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	12	19

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness95.0ms (0.6%)

Memory

16.2MiB live, 127.3MiB allocated

Rules

114×	`/-lowering-/.f32`
114×	`/-lowering-/.f64`
98×	`-lowering-.f32`
98×	`-lowering-.f64`
88×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	65	9
0	679	9
0	13	42
1	41	30
0	243	26
0	4	14
1	20	10
0	157	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

Stop Event

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

Compiler

Compiled 63 to 37 computations (41.3% saved)

preprocess41.0ms (0.3%)

Memory: -30.6MiB live, 90.8MiB allocated
Remove: (abs x)
Compiler: Compiled 66 to 32 computations (51.5% 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	23	380
1	44	380
2	96	380
3	155	380
4	172	380
5	218	380
6	263	380
7	294	380
8	363	380
9	383	380
10	383	380
0	383	380

Iter	Nodes	Cost
0	14	268
1	25	268
2	48	268
3	59	268
4	63	268
5	75	268
6	87	268
7	98	268
8	126	268
9	138	268
0	138	268

Iter	Nodes	Cost
0	10	27
1	65	9
0	679	9
0	13	42
1	41	30
0	243	26
0	4	14
1	20	10
0	157	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

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

Iter	Nodes	Cost
0	23	380
1	44	380
2	96	380
3	155	380
4	172	380
5	218	380
6	263	380
7	294	380
8	363	380
9	383	380
10	383	380
0	383	380

Iter	Nodes	Cost
0	14	268
1	25	268
2	48	268
3	59	268
4	63	268
5	75	268
6	87	268
7	98	268
8	126	268
9	138	268
0	138	268

Iter	Nodes	Cost
0	10	27
1	65	9
0	679	9
0	13	42
1	41	30
0	243	26
0	4	14
1	20	10
0	157	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148

analyze0.0ms (0%)

sample419.0ms (2.9%)

preprocess17.0ms (0.1%)

explain70.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize23.0ms (0.2%)

series3.0ms (0%)

rewrite47.0ms (0.3%)

simplify11.0ms (0.1%)

eval8.0ms (0.1%)

prune8.0ms (0.1%)

simplify4.0ms (0%)

localize41.0ms (0.3%)

series5.0ms (0%)

rewrite33.0ms (0.2%)

simplify176.0ms (1.2%)

eval23.0ms (0.2%)

prune17.0ms (0.1%)

simplify359.0ms (2.5%)

localize12.5s (85.9%)

series3.0ms (0%)

rewrite62.0ms (0.4%)

simplify32.0ms (0.2%)

eval13.0ms (0.1%)

prune26.0ms (0.2%)

simplify340.0ms (2.3%)

localize35.0ms (0.2%)

series1.0ms (0%)

rewrite38.0ms (0.3%)

simplify16.0ms (0.1%)

eval7.0ms (0.1%)

prune8.0ms (0.1%)

regimes16.0ms (0.1%)

regimes13.0ms (0.1%)

regimes11.0ms (0.1%)

regimes6.0ms (0%)

regimes20.0ms (0.1%)

simplify7.0ms (0%)

soundness95.0ms (0.6%)

preprocess41.0ms (0.3%)

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	23	380
1	44	380
2	96	380
3	155	380
4	172	380
5	218	380
6	263	380
7	294	380
8	363	380
9	383	380
10	383	380
0	383	380

Iter	Nodes	Cost
0	14	268
1	25	268
2	48	268
3	59	268
4	63	268
5	75	268
6	87	268
7	98	268
8	126	268
9	138	268
0	138	268

Iter	Nodes	Cost
0	10	27
1	65	9
0	679	9
0	13	42
1	41	30
0	243	26
0	4	14
1	20	10
0	157	9
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148