Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample550.0ms (64.9%)

Memory

17.0MiB live, 566.0MiB allocated; 174ms collecting garbage

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 177.0ms

ival-pow2: 86.0ms (48.7% of total)

ival-sqrt: 71.0ms (40.2% of total)

ival-add!: 19.0ms (10.8% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess85.0ms (10%)

Memory

42.6MiB live, 42.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	25	19
2	72	19
3	189	19
4	609	19
5	3566	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.2%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Symmetry

(abs x)

Compiler

Compiled 16 to 10 computations (37.5% saved)

series14.0ms (1.6%)

Memory

-40.5MiB live, 5.7MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51

Stop Event

1×	iter-limit

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

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)
4.0ms	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

6.0ms

inf

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

4.0ms

-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)

rewrite20.0ms (2.3%)

Memory

21.8MiB live, 21.8MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	20
0	8	16
0	35	13

Stop Event

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

Counts

5 → 21

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

eval2.0ms (0.3%)

Memory: 4.5MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 260 to 67 computations (74.2% saved)

prune2.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	4	24

Accuracy

100.0%

Counts

24 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.2%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 37 to 27 computations (27% saved)

series5.0ms (0.6%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	47

Stop Event

1×	iter-limit

Counts

12 → 5

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* -1 (* x (sqrt 2))) -1 (* x (sqrt 2)) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* -1 (* x (sqrt 2))) -1 (* x (sqrt 2)) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x) (sqrt (+ (* x x) (* x x))))
1.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* -1 (* x (sqrt 2))) -1 (* x (sqrt 2)) x (sqrt 2) 2 (sqrt (+ (pow x 2) (pow x 2))) (sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

2.0ms

inf

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

1.0ms

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

1.0ms

-inf

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

rewrite25.0ms (2.9%)

Memory

-40.3MiB live, 14.3MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
0	23	45
0	72	45

Stop Event

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

Counts

12 → 74

Calls

Call 1

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

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

eval5.0ms (0.6%)

Memory: 7.5MiB live, 7.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 564 to 134 computations (76.2% saved)

prune3.0ms (0.3%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	56	4	60

Accuracy

100.0%

Counts

60 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	55.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 36 to 25 computations (30.6% saved)

series6.0ms (0.7%)

Memory

9.7MiB live, 9.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	46

Stop Event

1×	iter-limit

Counts

9 → 5

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite18.0ms (2.1%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	41
0	18	39
0	69	33

Stop Event

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

Counts

9 → 35

Calls

Call 1

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

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

eval3.0ms (0.4%)

Memory: 3.3MiB live, 3.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 379 to 109 computations (71.2% saved)

prune2.0ms (0.2%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	31	5	36

Accuracy

100.0%

Counts

36 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	55.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 43 to 30 computations (30.2% saved)

series22.0ms (2.5%)

Memory

-42.9MiB live, 3.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	104

Stop Event

1×	iter-limit

Counts

5 → 10

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)

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

Calls

3 calls:

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

rewrite19.0ms (2.2%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	9	16
0	34	16

Stop Event

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

Counts

5 → 16

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)

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

eval1.0ms (0.2%)

Memory: 1.7MiB live, 1.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 244 to 79 computations (67.6% saved)

prune2.0ms (0.2%)

Memory

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

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	19	6	25

Accuracy

100.0%

Counts

25 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.5%	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	99.3%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
✓	55.3%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	2.2%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 57 to 40 computations (29.8% saved)

regimes34.0ms (4.1%)

Memory

22.6MiB live, 67.4MiB allocated; 4ms collecting garbage

Accuracy

Total -62.1b remaining (-7611%)

Threshold costs -62.1b (-7611%)

Counts

5 → 1

7 → 1

9 → 1

Calls

Call 1

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

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

Call 2

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

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

Call 3

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

Outputs
(hypot.f64 x x)

Calls

12 calls:

6.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
4.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	x
3.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (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
99.3%	1	`(pow.f64 x #s(literal 2 binary64))`
99.3%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.3%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.3%	1	`x`
99.5%	1	`(pow.f64 x #s(literal 2 binary64))`
99.5%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.5%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.5%	1	`x`
100.0%	1	`(pow.f64 x #s(literal 2 binary64))`
100.0%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
100.0%	1	`x`

Compiler

Compiled 143 to 74 computations (48.3% saved)

derivations3.0ms (0.4%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 23 to 14 computations (39.1% saved)

preprocess28.0ms (3.3%)

Memory: 12.5MiB live, 57.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 77 to 51 computations (33.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample550.0ms (64.9%)

preprocess85.0ms (10%)

series14.0ms (1.6%)

rewrite20.0ms (2.3%)

eval2.0ms (0.3%)

prune2.0ms (0.2%)

series5.0ms (0.6%)

rewrite25.0ms (2.9%)

eval5.0ms (0.6%)

prune3.0ms (0.3%)

series6.0ms (0.7%)

rewrite18.0ms (2.1%)

eval3.0ms (0.4%)

prune2.0ms (0.2%)

series22.0ms (2.5%)

rewrite19.0ms (2.2%)

eval1.0ms (0.2%)

prune2.0ms (0.2%)

regimes34.0ms (4.1%)

derivations3.0ms (0.4%)

preprocess28.0ms (3.3%)

end0.0ms (0%)

Profiling