Metrics for sqrt D (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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 8 to 7 computations (12.5% saved)

sample599.0ms (47.2%)

Memory

7.2MiB live, 487.0MiB allocated; 99ms collecting garbage

Samples

407.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 187.0ms

ival-pow2: 93.0ms (49.7% of total)

ival-sqrt: 55.0ms (29.4% of total)

ival-mult!: 38.0ms (20.3% of total)

adjust: 1.0ms (0.5% of total)

Bogosity

explain56.0ms (4.4%)

Memory

21.9MiB live, 68.5MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	7	(3.12570564774667e-158)	`(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))))`	oflow-rescue	64	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	64
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	64
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	54	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	54
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	54

Confusion

	Predicted +	Predicted -
+	118	7
-	0	131

Precision

1.0

Recall

0.944

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	118	0	7
-	0	0	131

Precision?

1.0

Recall?

0.944

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-pow2: 9.0ms (60.5% of total)

ival-sqrt: 3.0ms (20.2% of total)

ival-mult!: 2.0ms (13.4% of total)

adjust: 0.0ms (0% of total)

preprocess325.0ms (25.6%)

Memory

-21.8MiB live, 171.9MiB allocated; 59ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	19
2	55	19
3	167	19
4	408	19
5	1304	19
6	5101	19
0	5	6
0	8	6
1	13	6
2	34	6
3	106	6
4	358	6
5	1096	6
6	4530	6
0	8083	3

Stop Event

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

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))))
(hypot.f64 x x)

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% 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

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.3%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Counts

5 → 5

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

Calls

3 calls:

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

rewrite36.0ms (2.8%)

Memory

-19.1MiB live, 26.9MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	60
1	42	54
0	138	49

Stop Event

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

Counts

10 → 46

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

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

eval5.0ms (0.4%)

Memory: 6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 406 to 112 computations (72.4% saved)

prune2.0ms (0.2%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.6%	(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	56.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 28 to 17 computations (39.3% saved)

series42.0ms (3.3%)

Memory

3.7MiB live, 48.9MiB allocated; 4ms collecting garbage

Counts

13 → 14

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 x (+.f64 x x))
x
(+.f64 x x)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
#s(literal 1/4 binary64)
(hypot.f64 x x)

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

Calls

3 calls:

Time	Variable		Point	Expression
25.0ms	x	@	0	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))
10.0ms	x	@	inf	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))
8.0ms	x	@	-inf	((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

25.0ms

((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))

10.0ms

inf

((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))

8.0ms

-inf

((sqrt (* x (+ x x))) (* x (+ x x)) x (+ x x) (* (sqrt 2) x) (sqrt 2) 2 (* (pow (* (* x x) 2) 1/4) (pow (* (* x x) 2) 1/4)) (pow (* (* x x) 2) 1/4) (* (* x x) 2) (* x x) 1/4 (sqrt (+ (* x x) (* x x))))

rewrite25.0ms (2%)

Memory

19.3MiB live, 19.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	221
0	62	171
0	147	171

Stop Event

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

Counts

27 → 132

Calls

Call 1

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

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

eval32.0ms (2.6%)

Memory: -24.9MiB live, 22.8MiB allocated; 17ms collecting garbage
Compiler: Compiled 1 167 to 192 computations (83.5% saved)

prune3.0ms (0.2%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	101	4	105

Accuracy

100.0%

Counts

105 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.1%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 20 to 16 computations (20% saved)

series4.0ms (0.3%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Counts

6 → 8

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite20.0ms (1.6%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	99
0	38	82
0	90	82

Stop Event

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

Counts

14 → 23

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 3.4MiB live, 3.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 221 to 61 computations (72.4% saved)

prune2.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	24	5	29

Accuracy

100.0%

Counts

29 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.1%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
▶	99.1%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 28 to 21 computations (25% saved)

series4.0ms (0.4%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Counts

9 → 12

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) 2)
1.0ms	x	@	inf	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) 2)
1.0ms	x	@	0	((* (sqrt x) (sqrt (+ x x))) (sqrt x) x (sqrt (+ x x)) (+ x x) (* (sqrt x) (* (sqrt x) (sqrt 2))) (* (sqrt x) (sqrt 2)) (sqrt 2) 2)

Time

Variable

Point

Expression

3.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite24.0ms (1.9%)

Memory

-29.9MiB live, 16.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
0	56	139
0	137	139

Stop Event

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

Counts

21 → 43

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 474 to 109 computations (77% saved)

prune3.0ms (0.3%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	48	5	53

Accuracy

100.0%

Counts

53 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.1%	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
✓	99.1%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 84 to 45 computations (46.4% saved)

regimes10.0ms (0.8%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(hypot.f64 x x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

3.0ms	x
2.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
2.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes11.0ms (0.9%)

Memory

-33.9MiB live, 12.6MiB allocated; 2ms collecting garbage

Accuracy

Total -28.1b remaining (-6915.5%)

Threshold costs -28.1b (-6915.5%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
2.0ms	x
2.0ms	(pow.f64 x #s(literal 2 binary64))
2.0ms	(sqrt.f64 (*.f64 #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 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
99.4%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
99.4%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify35.0ms (2.7%)

Memory

29.8MiB live, 29.8MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	10	7
3	16	7
4	48	7
5	370	7
6	3460	7

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations2.0ms (0.2%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 7 to 5 computations (28.6% saved)

preprocess17.0ms (1.3%)

Memory: -27.0MiB live, 19.1MiB allocated; 3ms collecting garbage
Remove: (abs x)
Compiler: Compiled 32 to 24 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample599.0ms (47.2%)

explain56.0ms (4.4%)

preprocess325.0ms (25.6%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.3%)

rewrite36.0ms (2.8%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series42.0ms (3.3%)

rewrite25.0ms (2%)

eval32.0ms (2.6%)

prune3.0ms (0.2%)

series4.0ms (0.3%)

rewrite20.0ms (1.6%)

eval2.0ms (0.2%)

prune2.0ms (0.1%)

series4.0ms (0.4%)

rewrite24.0ms (1.9%)

eval4.0ms (0.3%)

prune3.0ms (0.3%)

regimes10.0ms (0.8%)

regimes11.0ms (0.9%)

simplify35.0ms (2.7%)

derivations2.0ms (0.2%)

preprocess17.0ms (1.3%)

end0.0ms (0%)

Profiling