Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample818.0ms (56.1%)

Memory

-1.1MiB live, 640.2MiB allocated; 730ms collecting garbage

Samples

350.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-pow2: 113.0ms (53.3% of total)

ival-sqrt: 77.0ms (36.3% of total)

ival-add!: 21.0ms (9.9% of total)

adjust: 2.0ms (0.9% of total)

Bogosity

explain61.0ms (4.2%)

Memory

29.5MiB live, 76.4MiB allocated; 3ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
124	-	5	(4.974546383886052e-157)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	62	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	62
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	124
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	57	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	58
↳	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	overflow	1
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	116

Confusion

	Predicted +	Predicted -
+	119	5
-	0	132

Precision

1.0

Recall

0.9596774193548387

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	119	0	5
-	0	0	132

Precision?

1.0

Recall?

0.9596774193548387

Freqs

test

number	freq
0	137
1	119

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-pow2: 6.0ms (56.8% of total)

ival-sqrt: 3.0ms (28.4% of total)

ival-add!: 1.0ms (9.5% of total)

adjust: 0.0ms (0% of total)

preprocess196.0ms (13.5%)

Memory

-20.6MiB live, 125.6MiB allocated; 109ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	16	19
2	46	19
3	125	19
4	271	19
5	817	19
6	4664	19
0	5	8
0	8	6
1	12	6
2	28	6
3	80	6
4	244	6
5	826	6
6	5361	6
0	8499	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 8 to 5 computations (37.5% saved)

series4.0ms (0.3%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

rewrite58.0ms (4%)

Memory

-11.6MiB live, 34.2MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	22	56
1	50	36
0	246	36

Stop Event

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

Counts

10 → 27

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 4.3MiB live, 4.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 352 to 101 computations (71.3% saved)

prune2.0ms (0.2%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	4	39

Accuracy

99.7%

Counts

39 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.3%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
▶	56.0%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x)))
▶	5.4%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
▶	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 44 to 34 computations (22.7% saved)

series8.0ms (0.5%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

21 → 19

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (sqrt (+ (pow x 2) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow x 2) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#s(approx (+ 0 (pow x 4)) #s(hole binary64 (pow x 4)))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (+ (pow x 2) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (sqrt 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
3.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
2.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

Time

Variable

Point

Expression

3.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

3.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

2.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* (sqrt 2) x) (sqrt 2) 2 x (sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (sqrt (+ (pow x 2) (* x x))) (+ (pow x 2) (* x x)) (pow x 2) (* x x) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

rewrite73.0ms (5%)

Memory

12.4MiB live, 63.2MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	323
0	85	246
1	173	202
0	851	202

Stop Event

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

Counts

40 → 313

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (sqrt 2) x) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#s(approx (+ (pow x 2) (pow x 2)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (sqrt (+ (pow x 2) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (pow x 2) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* (pow x 3) (sqrt 2))))
#s(approx (* 2 (pow x 6)) #s(hole binary64 (* 2 (pow x 6))))
#s(approx (pow x 6) #s(hole binary64 (pow x 6)))
#s(approx (sqrt (+ 0 (pow x 4))) #s(hole binary64 (pow x 2)))
#s(approx (+ 0 (pow x 4)) #s(hole binary64 (pow x 4)))
#s(approx (pow x 4) #s(hole binary64 (pow x 4)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (+ (pow x 2) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (* 2 (pow x 6))) #s(hole binary64 (* -1 (* (pow x 3) (sqrt 2)))))

Outputs
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (.f64 x x))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (neg.f64 x) x))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 x x))
(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x x)))
(neg.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (neg.f64 x) x)))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
x
(*.f64 (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #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 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x x)))
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(+.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(.f64 (.f64 (*.f64 x x) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (*.f64 x x) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (neg.f64 x) (fabs.f64 x)) (*.f64 (neg.f64 x) (fabs.f64 x)))
(.f64 (.f64 (fabs.f64 x) (neg.f64 x)) (*.f64 (fabs.f64 x) (neg.f64 x)))
(.f64 (.f64 (fabs.f64 x) x) (*.f64 (fabs.f64 x) x))
(.f64 (.f64 x (fabs.f64 x)) (*.f64 x (fabs.f64 x)))
(.f64 (.f64 (neg.f64 x) x) (*.f64 (neg.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 (pow.f64 x #s(literal 3 binary64))))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (*.f64 x x)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) x)
(.f64 (.f64 x x) (*.f64 x x))
(*.f64 x (pow.f64 x #s(literal 3 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 x #s(literal 4 binary64))
(/.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 8 binary64)))) (neg.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (pow.f64 x #s(literal 12 binary64))) (neg.f64 (pow.f64 x #s(literal 8 binary64))))
(/.f64 (neg.f64 (pow.f64 x #s(literal 8 binary64))) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 x #s(literal 8 binary64)))
(fma.f64 (.f64 (.f64 x x) (neg.f64 x)) (neg.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (fabs.f64 x)) (fabs.f64 x) #s(literal 0 binary64))
(fma.f64 (.f64 (neg.f64 x) (fabs.f64 x)) (.f64 (neg.f64 x) (fabs.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (fabs.f64 x) (neg.f64 x)) (.f64 (fabs.f64 x) (neg.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (fabs.f64 x) x) (.f64 (fabs.f64 x) x) #s(literal 0 binary64))
(fma.f64 (.f64 x (fabs.f64 x)) (.f64 x (fabs.f64 x)) #s(literal 0 binary64))
(fma.f64 (.f64 (neg.f64 x) x) (.f64 (neg.f64 x) x) #s(literal 0 binary64))
(fma.f64 (neg.f64 x) (neg.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64))
(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) x #s(literal 0 binary64))
(fma.f64 (.f64 x x) (.f64 x x) #s(literal 0 binary64))
(fma.f64 x (pow.f64 x #s(literal 3 binary64)) #s(literal 0 binary64))
(-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 8 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 (neg.f64 x) x) (*.f64 x x)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 4 binary64)
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (* (sqrt 2) x) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx x x)
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x x))
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x x))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* 2 (pow x 6))) (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (* 2 (pow x 6)) (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64)))
#s(approx (pow x 6) (pow.f64 x #s(literal 6 binary64)))
#s(approx (sqrt (+ 0 (pow x 4))) (*.f64 x x))
#s(approx (+ 0 (pow x 4)) (pow.f64 x #s(literal 4 binary64)))
#s(approx (+ 0 (pow x 4)) (pow.f64 x #s(literal 4 binary64)))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (* 2 (pow x 6))) (neg.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (sqrt.f64 #s(literal 2 binary64)))))

eval19.0ms (1.3%)

Memory: -17.6MiB live, 27.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 3 018 to 627 computations (79.2% saved)

prune5.0ms (0.4%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	192	4	196

Accuracy

100.0%

Counts

196 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	5.4%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
▶	99.1%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
✓	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 46 to 30 computations (34.8% saved)

series5.0ms (0.3%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Counts

9 → 8

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (/ 2 (sqrt 2)) x) #s(hole binary64 (* 2 (/ x (sqrt 2)))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (+ (* x x) (* x x)) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))
1.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

Time

Variable

Point

Expression

2.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

1.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* (/ 2 (sqrt 2)) x) (/ 2 (sqrt 2)) 2 (sqrt 2) x (sqrt (+ (* x x) (* x x))) (+ (* x x) (* x x)) (* x x))

rewrite65.0ms (4.4%)

Memory

-21.2MiB live, 69.0MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	139
0	40	113
1	89	85
0	432	85

Stop Event

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

Counts

17 → 80

Calls

Call 1

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

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

eval9.0ms (0.6%)

Memory: 19.7MiB live, 19.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 373 to 286 computations (79.2% saved)

prune4.0ms (0.3%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	91	4	95

Accuracy

100.0%

Counts

95 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	5.4%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
▶	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
✓	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 46 to 30 computations (34.8% saved)

series3.0ms (0.2%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Counts

6 → 5

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (/ (* 2 x) (sqrt 2)) #s(hole binary64 (* 2 (/ x (sqrt 2)))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2))

1.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2))

1.0ms

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2))

rewrite52.0ms (3.6%)

Memory

-26.0MiB live, 72.0MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	79
0	27	72
1	64	60
0	305	60

Stop Event

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

Counts

11 → 44

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 11.0MiB live, 11.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 883 to 159 computations (82% saved)

prune4.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	45	4	49

Accuracy

100.0%

Counts

49 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.0%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
✓	5.4%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
✓	99.4%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))

Compiler

Compiled 151 to 68 computations (55% saved)

regimes41.0ms (2.8%)

Memory

-28.9MiB live, 15.1MiB allocated; 9ms collecting garbage

Counts

9 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) x))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))

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

Calls

4 calls:

33.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	x
3.0ms	(pow.f64 x #s(literal 2 binary64))
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Results

Accuracy	Segments	Branch
99.4%	1	`(pow.f64 x #s(literal 2 binary64))`
99.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0.3%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
5.4%	1	`(pow.f64 x #s(literal 2 binary64))`
5.4%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
5.4%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
5.4%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

derivations3.0ms (0.2%)

Memory

2.1MiB live, 2.1MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 23 to 11 computations (52.2% saved)

preprocess14.0ms (0.9%)

Memory: 15.8MiB live, 15.8MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 108 to 64 computations (40.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample818.0ms (56.1%)

explain61.0ms (4.2%)

preprocess196.0ms (13.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite58.0ms (4%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

series8.0ms (0.5%)

rewrite73.0ms (5%)

eval19.0ms (1.3%)

prune5.0ms (0.4%)

series5.0ms (0.3%)

rewrite65.0ms (4.4%)

eval9.0ms (0.6%)

prune4.0ms (0.3%)

series3.0ms (0.2%)

rewrite52.0ms (3.6%)

eval4.0ms (0.3%)

prune4.0ms (0.2%)

regimes41.0ms (2.8%)

regimes4.0ms (0.3%)

derivations3.0ms (0.2%)

preprocess14.0ms (0.9%)

end0.0ms (0%)

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