Metrics for sqrt E (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 6 computations (40% saved)

sample497.0ms (20.8%)

Memory

21.9MiB live, 704.0MiB allocated

Samples

354.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 195.0ms

ival-pow2: 92.0ms (47.2% of total)

ival-sqrt: 55.0ms (28.2% of total)

ival-add: 40.0ms (20.5% of total)

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

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

Bogosity

preprocess15.0ms (0.6%)

Memory

18.7MiB live, 18.7MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	35	13
3	146	13
4	286	13
5	313	13
6	315	13
0	5	6
1	7	6
2	12	6
3	15	6
0	15	3

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

explain84.0ms (3.5%)

Memory

-19.5MiB live, 112.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
127	-	1	(-1.1434135325736018e-156)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	76	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	76
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	152
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	50	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	50
↳	`(pow.f64 x #s(literal 2 binary64))`	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

26.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.1%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize21.0ms (0.9%)

Memory

-12.0MiB live, 26.4MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

11.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

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

ival-pow2: 3.0ms (49.9% of total)

ival-sqrt: 2.0ms (33.3% of total)

ival-add: 1.0ms (16.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

3 → 36

Calls

Call 1

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

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

Calls

9 calls:

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

rewrite38.0ms (1.6%)

Memory

-0.9MiB live, 42.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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

simplify8.0ms (0.4%)

Memory

13.4MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

eval12.0ms (0.5%)

Memory: -21.4MiB live, 16.7MiB allocated
Compiler: Compiled 726 to 105 computations (85.5% saved)

prune6.0ms (0.2%)

Memory

12.1MiB live, 12.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Accuracy

100.0%

Counts

88 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	45.9%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
▶	54.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	55.4%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify18.0ms (0.7%)

Memory

-18.3MiB live, 20.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

208×	`accelerator-lowering-fma.f32`
208×	`accelerator-lowering-fma.f64`
168×	`-lowering-.f32`
168×	`-lowering-.f64`
94×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	23	43
2	35	43
3	45	43
4	57	43
5	69	43
6	80	43
7	103	43
8	118	43
9	127	43
10	205	43
11	347	43
12	361	43
13	361	43
0	361	37

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize36.0ms (1.5%)

Memory

12.5MiB live, 50.5MiB allocated

Localize:

Found 9 expressions of interest:

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

Samples

23.0ms

256×

valid

Compiler

Compiled 42 to 11 computations (73.8% saved)

Precisions

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

ival-hypot: 6.0ms (39.7% of total)

ival-sqrt: 4.0ms (26.5% of total)

ival-mult: 3.0ms (19.9% of total)

ival-add: 1.0ms (6.6% of total)

ival-neg: 1.0ms (6.6% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated

Counts

7 → 72

Calls

Call 1

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

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

Calls

18 calls:

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

rewrite37.0ms (1.5%)

Memory

-1.0MiB live, 40.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

114×	`-lowering-.f32`
114×	`-lowering-.f64`
70×	`accelerator-lowering-fma.f32`
70×	`accelerator-lowering-fma.f64`
62×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	46	25
0	274	23

Stop Event

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

Counts

7 → 101

Calls

Call 1

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

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

simplify11.0ms (0.5%)

Memory

19.0MiB live, 19.0MiB 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	9	308
1	17	308
2	32	308
3	36	308
4	40	308
5	52	308
6	64	308
7	75	308
8	95	308
9	100	308
0	100	308

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

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

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

eval19.0ms (0.8%)

Memory: -6.7MiB live, 31.8MiB allocated
Compiler: Compiled 1 491 to 195 computations (86.9% saved)

prune14.0ms (0.6%)

Memory

-12.4MiB live, 25.3MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	187	8	195

Accuracy

100.0%

Counts

195 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	45.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	45.9%	(*.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))))
▶	3.1%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	55.4%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	55.3%	(neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify414.0ms (17.3%)

Memory

27.8MiB live, 424.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))
✓	cost-diff	0	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	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))
✓	cost-diff	0	(*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	cost-diff	12480	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Rules

12 796×	`accelerator-lowering-fma.f32`
12 796×	`accelerator-lowering-fma.f64`
5 670×	`-lowering-.f32`
5 670×	`-lowering-.f64`
1 480×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	99
1	45	88
2	119	82
3	284	74
4	425	74
5	1143	74
6	2543	74
7	3508	74
8	5628	74
0	8049	71

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(neg (* x (exp (* (log 2) 1/2))))
(* x (exp (* (log 2) 1/2)))
x
(exp (* (log 2) 1/2))
(* (log 2) 1/2)
(log 2)
2
1/2
(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)
(* (sqrt (+ x x)) (sqrt x))
(sqrt (+ x x))
(+ x x)
x
(sqrt x)

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

localize66.0ms (2.8%)

Memory

-7.6MiB live, 108.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x))
✓	accuracy	100.0%	(.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) (+.f64 x x)) x)
✓	accuracy	80.3%	(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	68.6%	(/.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))
✓	accuracy	100.0%	(neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.3%	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))

Samples

22.0ms	140×	0	invalid
17.0ms	116×	0	valid

Compiler

Compiled 114 to 21 computations (81.6% saved)

Precisions

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

ival-mult: 8.0ms (30% of total)

ival-sqrt: 7.0ms (26.3% of total)

ival-exp: 3.0ms (11.3% of total)

ival-log: 3.0ms (11.3% of total)

ival-div: 2.0ms (7.5% of total)

ival-add: 2.0ms (7.5% of total)

ival-neg: 1.0ms (3.8% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

14 → 132

Calls

Call 1

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

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

33 calls:

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

rewrite39.0ms (1.6%)

Memory

-4.3MiB live, 39.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

122×	`-lowering-.f32`
122×	`-lowering-.f64`
118×	`/-lowering-/.f32`
118×	`/-lowering-/.f64`
66×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	53
1	87	29
0	725	29

Stop Event

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

Counts

14 → 54

Calls

Call 1

Inputs
(exp (* (log 2) 1/2))
(neg (* x (exp (* (log 2) 1/2))))
(* x (exp (* (log 2) 1/2)))
(* (log 2) 1/2)
(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)
(* (sqrt (+ x x)) (sqrt x))
(sqrt x)
(log 2)
(* (+ (* x x) 0) (+ x x))

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

simplify237.0ms (9.9%)

Memory

4.9MiB live, 81.8MiB allocated

Algorithm

1×	egg-herbie

Rules

2 058×	`associate-r`
1 620×	`-lowering-.f32`
1 620×	`-lowering-.f64`
1 616×	`accelerator-lowering-fma.f32`
1 616×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	576
1	60	576
2	151	576
3	275	576
4	507	576
5	827	576
6	1359	576
7	1483	576
8	1546	576
9	1604	576
10	1853	576
11	2109	576
12	2165	576
13	2185	576
14	2189	576
15	2189	576
16	2189	576
17	2405	576
18	2695	576
19	3564	576
20	3718	576
21	3822	576
22	3842	576
23	3842	576
24	3842	576
25	3862	576
26	3870	576
27	3870	576
28	4284	576
29	4896	576
30	4912	576
0	4912	576

Stop Event

1×	iter limit
1×	saturated

Counts

132 → 132

Calls

Call 1

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

eval44.0ms (1.8%)

Memory: 2.8MiB live, 41.6MiB allocated
Compiler: Compiled 2 861 to 275 computations (90.4% saved)

prune30.0ms (1.3%)

Memory

-5.1MiB live, 35.3MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	258	9	267

Accuracy

100.0%

Counts

267 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	45.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	45.9%	(*.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)))
✓	3.1%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	55.4%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	55.3%	(neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
▶	3.5%	#s(literal 0 binary64)

Compiler

Compiled 62 to 42 computations (32.3% saved)

simplify331.0ms (13.8%)

Memory

-2.2MiB live, 362.3MiB 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)

localize66.0ms (2.7%)

Memory

-19.6MiB live, 56.6MiB 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

53.0ms

256×

valid

Compiler

Compiled 62 to 11 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-sqrt: 36.0ms (78.3% of total)

ival-mult: 5.0ms (10.9% of total)

ival-add: 4.0ms (8.7% of total)

ival-div: 2.0ms (4.4% 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

1.9MiB live, 1.9MiB 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	(sqrt (/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x)))
0.0ms	x	@	inf	(/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x))
0.0ms	x	@	0	(sqrt (/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x)))
0.0ms	x	@	-inf	(/ (* (* (+ (* x x) 0) (+ x x)) x) (* x x))

rewrite37.0ms (1.5%)

Memory

3.2MiB live, 46.2MiB 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)

simplify11.0ms (0.5%)

Memory

17.3MiB live, 17.3MiB 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)))

eval10.0ms (0.4%)

Memory: -12.3MiB live, 25.9MiB allocated
Compiler: Compiled 1 094 to 152 computations (86.1% saved)

prune9.0ms (0.4%)

Memory

-8.4MiB live, 30.6MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	0	0
Picked	1	1	2
Done	0	7	7
Total	86	9	95

Accuracy

100.0%

Counts

95 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	45.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	45.9%	(*.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)))
✓	3.1%	(sqrt.f64 (+.f64 x x))
✓	54.1%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	55.4%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	55.3%	(neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
✓	3.5%	#s(literal 0 binary64)

Compiler

Compiled 153 to 74 computations (51.6% saved)

regimes18.0ms (0.8%)

Memory

4.5MiB live, 43.2MiB allocated

Counts

12 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

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

Results

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes18.0ms (0.8%)

Memory

-3.7MiB live, 36.9MiB allocated

Counts

9 → 2

Calls

Call 1

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

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	x
3.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
79.9%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
79.9%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
79.9%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes3.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.3%)

Memory

17.8MiB live, 17.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
45.9%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
45.9%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
45.9%	1	`(pow.f64 x #s(literal 2 binary64))`
45.9%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes9.0ms (0.4%)

Memory

-17.6MiB live, 17.6MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
5.1%	2	`x`
3.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.5%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes5.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)

Outputs
#s(literal 0 binary64)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.5%	1	`(pow.f64 x #s(literal 2 binary64))`
3.5%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch14.0ms (0.6%)

Memory

-9.2MiB live, 28.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-2.719997322683207e-293	7.918877166043363e-307

Samples

8.0ms

160×

valid

Compiler

Compiled 172 to 128 computations (25.6% saved)

Precisions

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

ival-pow2: 4.0ms (72.6% of total)

ival-add: 1.0ms (18.2% of total)

ival-sqrt: 1.0ms (18.2% of total)

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

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

bsearch15.0ms (0.6%)

Memory

-7.9MiB live, 30.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-2.719997322683207e-293	7.918877166043363e-307

Samples

9.0ms

160×

valid

Compiler

Compiled 142 to 118 computations (16.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-pow2: 2.0ms (55% of total)

ival-add: 1.0ms (27.5% of total)

ival-sqrt: 1.0ms (27.5% of total)

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

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

bsearch21.0ms (0.9%)

Memory

-16.9MiB live, 32.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	6.711906799865404e-208	3.3710941053474126e-196

Samples

6.0ms

160×

valid

Compiler

Compiled 102 to 78 computations (23.5% saved)

Precisions

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

ival-pow2: 2.0ms (57.7% of total)

ival-add: 1.0ms (28.8% of total)

ival-sqrt: 1.0ms (28.8% of total)

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

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

simplify8.0ms (0.3%)

Memory

23.2MiB live, 23.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	27	46
2	36	46
3	41	46
4	43	46

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 3569553643807187/90368446678662959902371482950548091627243325179250480789868861787606202571558351996987965471847359903068731695945087890499945499708108510324049698831582275405785474927446915858324226319766512887160235503322704971703517184 binary64)) #s(literal 0 binary64) (sqrt.f64 (+.f64 x x)))
#s(literal 0 binary64)

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(if (<=.f64 x #s(literal 3569553643807187/90368446678662959902371482950548091627243325179250480789868861787606202571558351996987965471847359903068731695945087890499945499708108510324049698831582275405785474927446915858324226319766512887160235503322704971703517184 binary64)) #s(literal 0 binary64) (sqrt.f64 (+.f64 x x)))
#s(literal 0 binary64)

soundness112.0ms (4.7%)

Memory

15.1MiB live, 205.4MiB allocated

Rules

122×	`-lowering-.f32`
122×	`-lowering-.f64`
118×	`/-lowering-/.f32`
118×	`/-lowering-/.f64`
114×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	5	14
1	25	10
0	167	9
0	11	33
1	46	25
0	274	23
0	19	53
1	87	29
0	725	29

Stop Event

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

Compiler

Compiled 121 to 68 computations (43.8% saved)

preprocess39.0ms (1.6%)

Memory: -11.2MiB live, 107.2MiB allocated
Compiler: Compiled 112 to 46 computations (58.9% 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	11	43
1	23	43
2	35	43
3	45	43
4	57	43
5	69	43
6	80	43
7	103	43
8	118	43
9	127	43
10	205	43
11	347	43
12	361	43
13	361	43
0	361	37

Iter	Nodes	Cost
0	9	308
1	17	308
2	32	308
3	36	308
4	40	308
5	52	308
6	64	308
7	75	308
8	95	308
9	100	308
0	100	308

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	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	5	14
1	25	10
0	167	9
0	11	33
1	46	25
0	274	23
0	19	53
1	87	29
0	725	29

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	11	43
1	23	43
2	35	43
3	45	43
4	57	43
5	69	43
6	80	43
7	103	43
8	118	43
9	127	43
10	205	43
11	347	43
12	361	43
13	361	43
0	361	37

Iter	Nodes	Cost
0	9	308
1	17	308
2	32	308
3	36	308
4	40	308
5	52	308
6	64	308
7	75	308
8	95	308
9	100	308
0	100	308

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	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	5	14
1	25	10
0	167	9
0	11	33
1	46	25
0	274	23
0	19	53
1	87	29
0	725	29

analyze0.0ms (0%)

sample497.0ms (20.8%)

preprocess15.0ms (0.6%)

explain84.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize21.0ms (0.9%)

series3.0ms (0.1%)

rewrite38.0ms (1.6%)

simplify8.0ms (0.4%)

eval12.0ms (0.5%)

prune6.0ms (0.2%)

simplify18.0ms (0.7%)

localize36.0ms (1.5%)

series2.0ms (0.1%)

rewrite37.0ms (1.5%)

simplify11.0ms (0.5%)

eval19.0ms (0.8%)

prune14.0ms (0.6%)

simplify414.0ms (17.3%)

localize66.0ms (2.8%)

series6.0ms (0.2%)

rewrite39.0ms (1.6%)

simplify237.0ms (9.9%)

eval44.0ms (1.8%)

prune30.0ms (1.3%)

simplify331.0ms (13.8%)

localize66.0ms (2.7%)

series1.0ms (0%)

rewrite37.0ms (1.5%)

simplify11.0ms (0.5%)

eval10.0ms (0.4%)

prune9.0ms (0.4%)

regimes18.0ms (0.8%)

regimes18.0ms (0.8%)

regimes3.0ms (0.1%)

regimes8.0ms (0.3%)

regimes9.0ms (0.4%)

regimes5.0ms (0.2%)

bsearch14.0ms (0.6%)

bsearch15.0ms (0.6%)

bsearch21.0ms (0.9%)

simplify8.0ms (0.3%)

soundness112.0ms (4.7%)

preprocess39.0ms (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	11	43
1	23	43
2	35	43
3	45	43
4	57	43
5	69	43
6	80	43
7	103	43
8	118	43
9	127	43
10	205	43
11	347	43
12	361	43
13	361	43
0	361	37

Iter	Nodes	Cost
0	9	308
1	17	308
2	32	308
3	36	308
4	40	308
5	52	308
6	64	308
7	75	308
8	95	308
9	100	308
0	100	308

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	8	148
1	15	148
2	32	148
3	37	148
4	41	148
5	53	148
6	65	148
7	76	148
8	96	148
9	101	148
0	101	148
0	5	14
1	25	10
0	167	9
0	11	33
1	46	25
0	274	23
0	19	53
1	87	29
0	725	29