Metrics for sqrt E (should all be same)

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample557.0ms (37.8%)

Memory

55.3MiB live, 770.5MiB allocated

Samples

372.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-pow2: 107.0ms (45.7% of total)

ival-sqrt: 75.0ms (32% of total)

ival-add: 43.0ms (18.4% of total)

ival-true: 5.0ms (2.1% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

preprocess38.0ms (2.6%)

Memory

-26.5MiB live, 30.3MiB 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	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

explain74.0ms (5%)

Memory

-10.7MiB live, 103.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	5	(2.2944289584478695e-157)	`(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	64	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	64
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	128
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	56	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	56
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	112

Confusion

	Predicted +	Predicted -
+	120	5
-	0	131

Precision

1.0

Recall

0.96

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	120	0	5
-	0	0	131

Precision?

1.0

Recall?

0.96

Freqs

test

number	freq
0	136
1	120

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

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

ival-pow2: 10.0ms (61.4% of total)

ival-sqrt: 3.0ms (18.4% of total)

ival-add: 2.0ms (12.3% 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.7%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB 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×	`lower-*.f64`
14×	`lower-*.f32`
4×	`*-commutative`
4×	`count-2`
4×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	20
0	8	16
1	10	16
2	15	16
3	18	16
0	18	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize22.0ms (1.5%)

Memory

-7.7MiB live, 36.5MiB 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	55.7%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

256×

valid

Compiler

Compiled 22 to 7 computations (68.2% saved)

Precisions

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

ival-pow2: 3.0ms (45% of total)

ival-sqrt: 2.0ms (30% of total)

ival-add: 1.0ms (15% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.2%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())

Inputs

#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())

#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())

#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())

Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())) ())

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))

simplify7.0ms (0.5%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.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))))

rewrite39.0ms (2.6%)

Memory

1.9MiB live, 39.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

70×	`lower-*.f64`
70×	`lower-*.f32`
44×	`lower-fma.f64`
44×	`lower-fma.f32`
34×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	18
0	8	14
1	28	10
0	170	9

Stop Event

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

Counts

3 → 33

Calls

Call 1

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

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 (.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 (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)))

eval8.0ms (0.5%)

Memory: 14.3MiB live, 14.3MiB allocated
Compiler: Compiled 774 to 104 computations (86.6% saved)

prune10.0ms (0.7%)

Memory

-22.6MiB live, 15.3MiB 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)
▶	55.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	52.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	49.0%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 24 to 15 computations (37.5% saved)

simplify16.0ms (1.1%)

Memory

20.2MiB live, 20.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

208×	`lower-fma.f64`
208×	`lower-fma.f32`
168×	`lower-*.f32`
164×	`lower-*.f64`
86×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
0	23	54
1	35	54
2	47	54
3	57	54
4	69	54
5	81	54
6	92	54
7	115	54
8	130	54
9	139	54
10	217	54
11	358	54
12	373	54
13	373	54
0	373	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(hypot.f64 x x)
x

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

localize51.0ms (3.5%)

Memory

-14.5MiB live, 65.0MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(hypot.f64 x x)
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 x (+.f64 x x))
✓	accuracy	55.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	49.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Samples

35.0ms

256×

valid

Compiler

Compiled 63 to 14 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-sqrt: 5.0ms (23.2% of total)

ival-mult: 4.0ms (18.5% of total)

ival-hypot: 4.0ms (18.5% of total)

ival-neg: 3.0ms (13.9% of total)

ival-pow2: 3.0ms (13.9% of total)

ival-add: 2.0ms (9.3% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.3%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

9 → 96

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (sqrt.f64 #s(literal 2 binary64))) (patch (.f64 x (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x (+.f64 x x))) (patch (sqrt.f64 (.f64 x (+.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 x (+.f64 x x)) (patch (.f64 x (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (hypot.f64 x x) (patch (hypot.f64 x x) #<representation binary64>) () ())) ())

Calls

24 calls:

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

simplify9.0ms (0.6%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	412
1	17	412
2	32	412
3	36	412
4	40	412
5	52	412
6	64	412
7	75	412
8	95	412
9	100	412
0	100	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)))
(* -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)))
(* 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
(* 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))
(* -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))
(* 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))

rewrite37.0ms (2.5%)

Memory

-0.8MiB live, 37.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

122×	`lower-*.f32`
118×	`lower-*.f64`
76×	`lower-fma.f64`
76×	`lower-fma.f32`
62×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	23	44
1	65	40
0	298	40

Stop Event

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

Counts

9 → 107

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
(+.f64 x x)
(hypot.f64 x x)

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

eval22.0ms (1.5%)

Memory: 0.3MiB live, 38.0MiB allocated
Compiler: Compiled 1 799 to 201 computations (88.8% saved)

prune19.0ms (1.3%)

Memory

-1.3MiB live, 36.9MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	218	7	225

Accuracy

100.0%

Counts

225 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	51.7%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	3.7%	(sqrt.f64 (+.f64 x x))
✓	55.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	52.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.0%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
▶	48.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

Compiler

Compiled 47 to 31 computations (34% saved)

simplify21.0ms (1.4%)

Memory

-20.0MiB live, 22.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 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 x x)
✓	cost-diff	0	(sqrt.f64 (+.f64 x x))
✓	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	0	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (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

208×	`lower-fma.f64`
208×	`lower-fma.f32`
176×	`lower-*.f32`
170×	`lower-*.f64`
90×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	71
0	25	61
1	42	57
2	59	57
3	69	57
4	81	57
5	93	57
6	104	57
7	127	57
8	142	57
9	151	57
10	229	57
11	368	57
12	382	57
13	382	57
0	382	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize51.0ms (3.4%)

Memory

32.0MiB live, 70.0MiB allocated

Localize:

Found 10 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 x x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x x))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.6%	(.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	99.2%	(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	49.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

Samples

16.0ms	133×	0	valid
15.0ms	123×	0	invalid

Compiler

Compiled 64 to 17 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sqrt: 5.0ms (23.3% of total)

ival-mult: 4.0ms (18.7% of total)

ival-exp: 3.0ms (14% of total)

ival-log: 3.0ms (14% of total)

ival-pow2: 3.0ms (14% of total)

ival-add: 2.0ms (9.3% of total)

ival-neg: 1.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.5%)

Memory

-30.6MiB live, 7.4MiB allocated

Counts

9 → 84

Calls

Call 1

Inputs
#s(alt (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) (patch (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (log.f64 #s(literal 2 binary64)) (patch (log.f64 #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) (patch #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor 0 x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 2))) (taylor -inf x) (#s(alt (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) (patch (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) (patch (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 x x)) (patch (sqrt.f64 (+.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(sqrt (+ x x))
1.0ms	x	@	-inf	(sqrt (+ x x))
1.0ms	x	@	-inf	(* (sqrt (+ x x)) (sqrt x))
0.0ms	x	@	inf	(sqrt (+ x x))
0.0ms	x	@	-inf	(sqrt x)

simplify167.0ms (11.3%)

Memory

16.8MiB live, 95.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 194×	`associate-r`
944×	`lower-*.f64`
944×	`lower-fma.f64`
944×	`lower-fma.f32`
944×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	360
1	46	360
2	130	360
3	260	360
4	492	360
5	811	360
6	1343	360
7	1471	360
8	1521	360
9	1545	360
10	1680	360
11	1871	360
12	1913	360
13	1941	360
14	1945	360
15	1945	360
16	2183	360
17	2287	360
18	2907	360
19	3214	360
20	3226	360
0	3226	360

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

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)))
(* -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)
(* 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)))

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

rewrite40.0ms (2.7%)

Memory

5.1MiB live, 43.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

126×	`lower-*.f32`
120×	`lower-*.f64`
76×	`lower-fma.f64`
76×	`lower-fma.f32`
60×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	55
0	25	46
1	69	36
0	310	33

Stop Event

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

Counts

9 → 84

Calls

Call 1

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

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

eval22.0ms (1.5%)

Memory: 0.5MiB live, 37.6MiB allocated
Compiler: Compiled 2 090 to 211 computations (89.9% saved)

prune22.0ms (1.5%)

Memory

3.1MiB live, 41.0MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	235	7	242

Accuracy

100.0%

Counts

242 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	51.7%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	3.7%	(sqrt.f64 (+.f64 x x))
✓	55.7%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	52.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	49.0%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	48.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (exp.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))

Compiler

Compiled 96 to 52 computations (45.8% saved)

regimes12.0ms (0.8%)

Memory

16.2MiB live, 16.2MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (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))
(hypot.f64 x x)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (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:

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

Results

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

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes58.0ms (3.9%)

Memory

-30.4MiB live, 16.9MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(pow.f64 x #s(literal 2 binary64))
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)))

Results

Accuracy	Segments	Branch
99.5%	2	`x`
81.2%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
81.2%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
81.2%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes3.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.4%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	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
52.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
52.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
52.4%	1	`(pow.f64 x #s(literal 2 binary64))`
52.4%	1	`x`

Compiler

Compiled 23 to 13 computations (43.5% saved)

regimes9.0ms (0.6%)

Memory

-25.8MiB live, 12.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x x))

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

Calls

4 calls:

5.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	x
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
3.7%	1	`x`
3.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
3.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
3.7%	1	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 23 to 13 computations (43.5% saved)

bsearch13.0ms (0.9%)

Memory

25.7MiB live, 25.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-3.939075687837942e-296	1.9359173281210847e-307

Samples

6.0ms

160×

valid

Compiler

Compiled 182 to 128 computations (29.7% saved)

Precisions

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

ival-pow2: 2.0ms (55.8% of total)

ival-add: 1.0ms (27.9% of total)

ival-sqrt: 1.0ms (27.9% of total)

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

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

bsearch1.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-3.939075687837942e-296	1.9359173281210847e-307

Compiler

Compiled 162 to 118 computations (27.2% saved)

simplify11.0ms (0.7%)

Memory

-23.1MiB live, 15.1MiB 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	19	76
1	29	76
2	38	76
3	43	76
4	45	76

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 x x))

Outputs
(hypot.f64 x x)
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))) (.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 x x))

soundness82.0ms (5.5%)

Memory

4.0MiB live, 87.3MiB allocated

Rules

122×	`lower-*.f32`
118×	`lower-*.f64`
76×	`lower-fma.f64`
76×	`lower-fma.f32`
70×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	23	44
1	65	40
0	298	40
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	18
0	8	14
1	28	10
0	170	9

Stop Event

1×	done
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Compiler

Compiled 127 to 64 computations (49.6% saved)

preprocess32.0ms (2.1%)

Memory: -10.1MiB live, 66.8MiB allocated
Compiler: Compiled 108 to 40 computations (63% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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	14	67
0	23	54
1	35	54
2	47	54
3	57	54
4	69	54
5	81	54
6	92	54
7	115	54
8	130	54
9	139	54
10	217	54
11	358	54
12	373	54
13	373	54
0	373	54

Iter	Nodes	Cost
0	9	412
1	17	412
2	32	412
3	36	412
4	40	412
5	52	412
6	64	412
7	75	412
8	95	412
9	100	412
0	100	412

Iter	Nodes	Cost
0	16	71
0	25	61
1	42	57
2	59	57
3	69	57
4	81	57
5	93	57
6	104	57
7	127	57
8	142	57
9	151	57
10	229	57
11	368	57
12	382	57
13	382	57
0	382	54

Iter	Nodes	Cost
0	14	55
0	23	44
1	65	40
0	298	40
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	18
0	8	14
1	28	10
0	170	9

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	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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	14	67
0	23	54
1	35	54
2	47	54
3	57	54
4	69	54
5	81	54
6	92	54
7	115	54
8	130	54
9	139	54
10	217	54
11	358	54
12	373	54
13	373	54
0	373	54

Iter	Nodes	Cost
0	9	412
1	17	412
2	32	412
3	36	412
4	40	412
5	52	412
6	64	412
7	75	412
8	95	412
9	100	412
0	100	412

Iter	Nodes	Cost
0	16	71
0	25	61
1	42	57
2	59	57
3	69	57
4	81	57
5	93	57
6	104	57
7	127	57
8	142	57
9	151	57
10	229	57
11	368	57
12	382	57
13	382	57
0	382	54

Iter	Nodes	Cost
0	14	55
0	23	44
1	65	40
0	298	40
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	18
0	8	14
1	28	10
0	170	9

analyze0.0ms (0%)

sample557.0ms (37.8%)

preprocess38.0ms (2.6%)

explain74.0ms (5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.3%)

localize22.0ms (1.5%)

series3.0ms (0.2%)

simplify7.0ms (0.5%)

rewrite39.0ms (2.6%)

eval8.0ms (0.5%)

prune10.0ms (0.7%)

simplify16.0ms (1.1%)

localize51.0ms (3.5%)

series4.0ms (0.3%)

simplify9.0ms (0.6%)

rewrite37.0ms (2.5%)

eval22.0ms (1.5%)

prune19.0ms (1.3%)

simplify21.0ms (1.4%)

localize51.0ms (3.4%)

series8.0ms (0.5%)

simplify167.0ms (11.3%)

rewrite40.0ms (2.7%)

eval22.0ms (1.5%)

prune22.0ms (1.5%)

regimes12.0ms (0.8%)

regimes58.0ms (3.9%)

regimes3.0ms (0.2%)

regimes6.0ms (0.4%)

regimes9.0ms (0.6%)

bsearch13.0ms (0.9%)

bsearch1.0ms (0.1%)

simplify11.0ms (0.7%)

soundness82.0ms (5.5%)

preprocess32.0ms (2.1%)

end0.0ms (0%)

Profiling

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	8
0	8	6
1	10	6
2	15	6
3	18	6
0	18	3

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	14	67
0	23	54
1	35	54
2	47	54
3	57	54
4	69	54
5	81	54
6	92	54
7	115	54
8	130	54
9	139	54
10	217	54
11	358	54
12	373	54
13	373	54
0	373	54

Iter	Nodes	Cost
0	9	412
1	17	412
2	32	412
3	36	412
4	40	412
5	52	412
6	64	412
7	75	412
8	95	412
9	100	412
0	100	412

Iter	Nodes	Cost
0	16	71
0	25	61
1	42	57
2	59	57
3	69	57
4	81	57
5	93	57
6	104	57
7	127	57
8	142	57
9	151	57
10	229	57
11	368	57
12	382	57
13	382	57
0	382	54

Iter	Nodes	Cost
0	14	55
0	23	44
1	65	40
0	298	40
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	18
0	8	14
1	28	10
0	170	9