Metrics for sqrt D (should all be same)

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample841.0ms (7.7%)

Memory

39.0MiB live, 753.1MiB allocated

Samples

491.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 286.0ms

ival-pow2: 156.0ms (54.5% of total)

ival-sqrt: 61.0ms (21.3% of total)

ival-mult: 56.0ms (19.6% of total)

ival-true: 6.0ms (2.1% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

preprocess19.0ms (0.2%)

Memory

-11.2MiB live, 26.8MiB allocated

Algorithm

1×	egg-herbie

Rules

70×	`associate-r`
46×	`associate-l`
38×	`distribute-rgt-neg-out`
38×	`unsub-neg`
34×	`distribute-lft-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Stop Event

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

Calls

Call 1

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

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

explain65.0ms (0.6%)

Memory

-12.3MiB live, 107.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
114	-	3	(-7.11307426877938e-157)	`(sqrt.f64 (*.f64 #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 #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 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	57	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	57
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	57
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	54	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	54
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	54

Confusion

	Predicted +	Predicted -
+	111	3
-	0	142

Precision

1.0

Recall

0.9736842105263158

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	111	0	3
-	0	0	142

Precision?

1.0

Recall?

0.9736842105263158

Freqs

test

number	freq
0	145
1	111

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 50 to 24 computations (52% saved)

Precisions

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

ival-pow2: 6.0ms (39.4% of total)

ival-sqrt: 5.0ms (32.9% of total)

ival-mult: 3.0ms (19.7% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

14×	`lower-*.f32`
12×	`lower-*.f64`
8×	`*-commutative`
2×	`lift-sqrt.f64`
2×	`lift-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	10	16
2	14	16
3	16	16
0	16	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize39.0ms (0.4%)

Memory

-13.0MiB live, 22.5MiB 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 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
✓	accuracy	59.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Samples

12.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-pow2: 3.0ms (46.8% of total)

ival-sqrt: 2.0ms (31.2% of total)

ival-mult: 1.0ms (15.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

3 → 36

Calls

Call 1

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

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

Calls

9 calls:

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

simplify7.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB 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	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	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)
(* 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))

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

rewrite171.0ms (1.6%)

Memory

-16.9MiB live, 229.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 310×	`lower-*.f64`
2 310×	`lower-*.f32`
2 014×	`lower-/.f64`
2 014×	`lower-/.f32`
1 182×	`frac-times`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4

Stop Event

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

Counts

3 → 46

Calls

Call 1

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

Outputs
#s(literal 1 binary64)
x
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 16 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))))
(exp.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64)))))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64))))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 2 binary64)))))
(/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 #s(literal 0 binary64) (log.f64 #s(literal 1/2 binary64)))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (log.f64 #s(literal 1/2 binary64)))))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (E.f64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (log.f64 #s(literal 2 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)))
(pow.f64 (sqrt.f64 (E.f64)) (+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 16 binary64) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (log.f64 #s(literal 4 binary64)))
(pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (log.f64 #s(literal 2 binary64))))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal -2 binary64)))
(pow.f64 (pow.f64 (sqrt.f64 (E.f64)) (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (log.f64 #s(literal 1/2 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 1 binary64)))
#s(literal 2 binary64)

eval9.0ms (0.1%)

Memory: 10.0MiB live, 10.0MiB allocated
Compiler: Compiled 563 to 120 computations (78.7% saved)

prune7.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Accuracy

99.7%

Counts

83 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
▶	5.6%	(sqrt.f64 #s(literal 2 binary64))
▶	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 21 to 17 computations (19% saved)

simplify8.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	20	78
1	32	78
2	45	78
3	56	78
4	68	78
5	80	78
6	91	78
7	111	78
8	116	78
0	116	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize49.0ms (0.4%)

Memory

-27.3MiB live, 87.3MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
✓	accuracy	100.0%	#s(approx (pow x 2) (*.f64 x x))
✓	accuracy	59.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	53.9%	#s(approx (sqrt (* 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	99.3%	(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Samples

30.0ms

256×

valid

Compiler

Compiled 57 to 11 computations (80.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 6.0ms (43.6% of total)

ival-sqrt: 3.0ms (21.8% of total)

ival-pow2: 3.0ms (21.8% of total)

ival-neg: 1.0ms (7.3% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

9 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

simplify9.0ms (0.1%)

Memory

19.2MiB live, 19.2MiB 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	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

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))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite277.0ms (2.5%)

Memory

9.4MiB live, 366.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`
2 986×	`lower-*.f64`
1 314×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	63
0	20	67
1	47	59
2	115	59
3	502	59
4	4969	57
0	8327	57

Stop Event

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

Counts

9 → 1 159

Calls

Call 1

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

Outputs
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (neg.f64 x)))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) x))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (.f64 (neg.f64 x) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) x)))) (sqrt.f64 x)))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1 binary64)))
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(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)) (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64))))
(.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (*.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(approx (pow x 2) (*.f64 x x)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (*.f64 x x))) #s(literal 1/8 binary64)))
(.f64 (.f64 (.f64 (sqrt.f64 #s(approx (pow x 2) (.f64 x x))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (pow x 2) (.f64 x x)))) (sqrt.f64 #s(literal 2 binary64)))
(exp.f64 (log.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x)))
(.f64 #s(literal 2 binary64) (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))))
(.f64 #s(approx (pow x 2) (.f64 x x)) #s(literal 2 binary64))
(.f64 (exp.f64 (log.f64 #s(approx (pow x 2) (.f64 x x)))) #s(literal 2 binary64))
#s(approx (pow x 2) (*.f64 x x))
(+.f64 (*.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal 1 binary64))) (.f64 #s(literal 2 binary64) (log.f64 x))))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(fabs.f64 (neg.f64 (*.f64 x x)))
(fabs.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 x (.f64 x (*.f64 x x))))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (*.f64 x (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 x (sqrt.f64 x))) #s(literal 0 binary64))
(fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #s(literal 0 binary64))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 0 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 0 binary64)) (-.f64 (.f64 x x) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 x (log.f64 (exp.f64 #s(literal 2 binary64))))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 8 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 4 binary64) (log.f64 x)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (sqrt.f64 x) (.f64 x (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 x (sqrt.f64 x))))
(.f64 (.f64 x (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 #s(literal 3/2 binary64) (log.f64 x))) (sqrt.f64 x))
(.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)) #s(literal 2 binary64))))

eval221.0ms (2%)

Memory: 19.6MiB live, 439.2MiB allocated
Compiler: Compiled 29 010 to 1 701 computations (94.1% saved)

prune169.0ms (1.5%)

Memory

-21.9MiB live, 361.6MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	1 833	5	1 838
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 833	9	1 842

Accuracy

100.0%

Counts

1 842 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.6%	(sqrt.f64 #s(literal 2 binary64))
▶	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
▶	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
▶	48.0%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 119 to 85 computations (28.6% saved)

simplify220.0ms (2%)

Memory

-18.9MiB live, 135.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
✓	cost-diff	128	(neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))
✓	cost-diff	640	(/.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	2624	(.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	0	(sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	2240	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	128	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Rules

3 280×	`lower-*.f32`
3 268×	`lower-*.f64`
3 088×	`lower-fma.f64`
3 088×	`lower-fma.f32`
1 360×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	209
0	39	183
1	76	168
2	203	164
3	780	164
4	2755	164
5	5054	164
6	6422	164
7	7043	164
8	7269	164
9	7323	164
10	7399	164
11	7905	164
0	8162	164

Stop Event

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

Calls

Call 1

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

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

localize87.0ms (0.8%)

Memory

25.1MiB live, 136.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.5%	(.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	99.4%	(/.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.5%	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	53.9%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	100.0%	(*.f64 x #s(literal -2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.3%	(*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)
✓	accuracy	98.4%	(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	53.9%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	53.9%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

Samples

43.0ms

256×

valid

Compiler

Compiled 162 to 22 computations (86.4% saved)

Precisions

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

ival-mult: 10.0ms (38.2% of total)

ival-div: 6.0ms (22.9% of total)

ival-sqrt: 5.0ms (19.1% of total)

ival-pow2: 3.0ms (11.5% of total)

ival-neg: 2.0ms (7.6% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

17 → 168

Calls

Call 1

Inputs
#<alt (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x #s(literal -2 binary64))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))>
#<alt (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x)>
#<alt (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))>
#<alt (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))>
#<alt (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (/.f64 (.f64 #s(literal 2 binary64) x) (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 (/.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))) (/.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))))>

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

Calls

42 calls:

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

simplify16.0ms (0.1%)

Memory

-29.5MiB live, 16.0MiB allocated

Algorithm

1×	egg-herbie

Rules

56×	`lower-*.f64`
56×	`lower-*.f32`
52×	`lower-fma.f64`
52×	`lower-fma.f32`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	848
1	32	848
2	48	848
3	55	848
4	60	848
5	72	848
6	84	848
7	95	848
8	127	848
9	141	848
10	142	848
0	142	848

Stop Event

1×	iter limit
1×	saturated

Counts

168 → 168

Calls

Call 1

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

rewrite232.0ms (2.1%)

Memory

-17.9MiB live, 318.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 792×	`lower-*.f32`
2 780×	`lower-*.f64`
1 788×	`lower-/.f32`
1 780×	`lower-/.f64`
856×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	164
0	39	136
1	115	119
2	647	93
0	5224	93

Stop Event

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

Counts

17 → 2 177

Calls

Call 1

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

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

eval456.0ms (4.2%)

Memory: 54.2MiB live, 736.9MiB allocated
Compiler: Compiled 40 736 to 3 206 computations (92.1% saved)

prune286.0ms (2.6%)

Memory

-16.2MiB live, 592.8MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	3 144	2	3 146
Fresh	0	0	0
Picked	3	2	5
Done	0	4	4
Total	3 147	8	3 155

Accuracy

100.0%

Counts

3 155 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.6%	(sqrt.f64 #s(literal 2 binary64))
▶	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
▶	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 57 to 42 computations (26.3% saved)

simplify6.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	cost-diff	2624	(/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Rules

48×	`lower-*.f32`
44×	`lower-*.f64`
36×	`lower-/.f32`
30×	`lower-/.f64`
16×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	75
0	22	75
1	32	75
2	43	65
3	50	65
4	57	65
5	65	65
6	65	65
0	65	65

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize49.0ms (0.4%)

Memory

3.9MiB live, 79.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))
✓	accuracy	99.5%	(/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	48.4%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.4%	(/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	53.9%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

Samples

29.0ms

256×

valid

Compiler

Compiled 58 to 15 computations (74.1% saved)

Precisions

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

ival-sqrt: 8.0ms (39.4% of total)

ival-div: 5.0ms (24.6% of total)

ival-mult: 4.0ms (19.7% of total)

ival-pow2: 3.0ms (14.8% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

8 → 72

Calls

Call 1

Inputs
#<alt #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))>
#<alt (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))>
#<alt (*.f64 x #s(literal 2 binary64))>
#<alt (sqrt.f64 #s(literal 2 binary64))>
#<alt (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))))>
#<alt #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))>
#<alt (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))>
#<alt (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))>

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

Calls

18 calls:

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

simplify16.0ms (0.1%)

Memory

-23.8MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Rules

68×	`lower-*.f64`
68×	`lower-*.f32`
64×	`lower-fma.f64`
64×	`lower-fma.f32`
52×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	392
1	32	392
2	54	392
3	63	392
4	68	392
5	80	392
6	92	392
7	103	392
8	139	392
9	155	392
10	156	392
0	156	392

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

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

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

rewrite194.0ms (1.8%)

Memory

22.2MiB live, 332.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 338×	`lower-*.f32`
3 334×	`lower-*.f64`
2 264×	`lower-/.f32`
2 258×	`lower-/.f64`
1 518×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	22	65
1	66	49
2	293	49
3	1813	45
0	8549	45

Stop Event

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

Counts

8 → 648

Calls

Call 1

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

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

eval334.0ms (3%)

Memory: -18.5MiB live, 231.1MiB allocated
Compiler: Compiled 13 318 to 1 975 computations (85.2% saved)

prune99.0ms (0.9%)

Memory

4.8MiB live, 245.1MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	908	0	908
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	908	8	916

Accuracy

100.0%

Counts

916 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	59.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (pow x 2) (.f64 x x))))
✓	5.6%	(sqrt.f64 #s(literal 2 binary64))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (/.f64 x (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	53.6%	#s(approx (sqrt (* 2 (pow x 2))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (sqrt.f64 #s(literal 2 binary64)))))
✓	53.5%	#s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	48.1%	#s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 142 to 73 computations (48.6% saved)

regimes17.0ms (0.2%)

Memory

0.3MiB live, 39.0MiB allocated

Counts

12 → 2

Calls

Call 1

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

Outputs

#s(approx (sqrt (* 2 (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.4%	2	`x`
80.8%	3	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
80.8%	3	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
80.8%	3	`(pow.f64 x #s(literal 2 binary64))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Memory

-21.4MiB live, 17.8MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

4 calls:

2.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
53.5%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
53.5%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
53.5%	1	`(pow.f64 x #s(literal 2 binary64))`
55.3%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes5.0ms (0%)

Memory

13.7MiB live, 13.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.6%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
5.6%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
5.6%	1	`(pow.f64 x #s(literal 2 binary64))`
5.6%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch10.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	-2.897770144345041e-308	1.6357353678144262e-307

Samples

5.0ms

112×

valid

Compiler

Compiled 122 to 100 computations (18% saved)

Precisions

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

ival-mult: 1.0ms (37.1% of total)

ival-sqrt: 1.0ms (37.1% of total)

ival-pow2: 1.0ms (37.1% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-2.897770144345041e-308	1.6357353678144262e-307

Compiler

Compiled 108 to 93 computations (13.9% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-2.897770144345041e-308	1.6357353678144262e-307

Compiler

Compiled 101 to 86 computations (14.9% saved)

bsearch22.0ms (0.2%)

Memory

-26.4MiB live, 12.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	-5.201945387686553e-204	-1.173702054644167e-212

Samples

16.0ms

144×

valid

Compiler

Compiled 100 to 90 computations (10% saved)

Precisions

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

ival-mult: 10.0ms (77% of total)

ival-pow2: 2.0ms (15.4% of total)

ival-sqrt: 1.0ms (7.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify7.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-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	25	104
1	36	104
2	45	104
3	50	104
4	52	104

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (/.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (/.f64 (.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (neg.f64 (.f64 x (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt ( 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (* 2 (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

soundness7.0s (63.4%)

Memory

1.1MiB live, 379.7MiB allocated

Rules

3 310×	`lower-fma.f64`
3 310×	`lower-fma.f32`
2 992×	`lower-*.f32`
2 986×	`lower-*.f64`
2 792×	`lower-*.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	164
0	39	136
1	115	119
2	647	93
0	5224	93
0	5	14
0	8	14
1	22	12
2	57	12
3	186	12
4	765	4
5	6179	4
0	9030	4
0	14	63
0	20	67
1	47	59
2	115	59
3	502	59
4	4969	57
0	8327	57
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Stop Event

1×	done
1×	iter limit
1×	saturated
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 121 to 72 computations (40.5% saved)

preprocess35.0ms (0.3%)

Memory: 5.2MiB live, 80.4MiB allocated
Compiler: Compiled 126 to 46 computations (63.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	17	848
1	32	848
2	48	848
3	55	848
4	60	848
5	72	848
6	84	848
7	95	848
8	127	848
9	141	848
10	142	848
0	142	848

Iter	Nodes	Cost
0	16	392
1	32	392
2	54	392
3	63	392
4	68	392
5	80	392
6	92	392
7	103	392
8	139	392
9	155	392
10	156	392
0	156	392

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	17	848
1	32	848
2	48	848
3	55	848
4	60	848
5	72	848
6	84	848
7	95	848
8	127	848
9	141	848
10	142	848
0	142	848

Iter	Nodes	Cost
0	16	392
1	32	392
2	54	392
3	63	392
4	68	392
5	80	392
6	92	392
7	103	392
8	139	392
9	155	392
10	156	392
0	156	392

analyze0.0ms (0%)

sample841.0ms (7.7%)

preprocess19.0ms (0.2%)

explain65.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

localize39.0ms (0.4%)

series3.0ms (0%)

simplify7.0ms (0.1%)

rewrite171.0ms (1.6%)

eval9.0ms (0.1%)

prune7.0ms (0.1%)

simplify8.0ms (0.1%)

localize49.0ms (0.4%)

series2.0ms (0%)

simplify9.0ms (0.1%)

rewrite277.0ms (2.5%)

eval221.0ms (2%)

prune169.0ms (1.5%)

simplify220.0ms (2%)

localize87.0ms (0.8%)

series7.0ms (0.1%)

simplify16.0ms (0.1%)

rewrite232.0ms (2.1%)

eval456.0ms (4.2%)

prune286.0ms (2.6%)

simplify6.0ms (0.1%)

localize49.0ms (0.4%)

series2.0ms (0%)

simplify16.0ms (0.1%)

rewrite194.0ms (1.8%)

eval334.0ms (3%)

prune99.0ms (0.9%)

regimes17.0ms (0.2%)

regimes3.0ms (0%)

regimes3.0ms (0%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

bsearch10.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch22.0ms (0.2%)

simplify7.0ms (0.1%)

soundness7.0s (63.4%)

preprocess35.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	15
1	15	13
2	34	13
3	123	13
4	246	13
5	270	13
6	280	13
0	5	6
0	8	6
1	10	6
2	14	6
3	16	6
0	16	6

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	396
1	15	396
2	32	396
3	38	396
4	42	396
5	54	396
6	66	396
7	77	396
8	97	396
9	102	396
0	102	396

Iter	Nodes	Cost
0	17	848
1	32	848
2	48	848
3	55	848
4	60	848
5	72	848
6	84	848
7	95	848
8	127	848
9	141	848
10	142	848
0	142	848

Iter	Nodes	Cost
0	16	392
1	32	392
2	54	392
3	63	392
4	68	392
5	80	392
6	92	392
7	103	392
8	139	392
9	155	392
10	156	392
0	156	392