Metrics for sqrt A (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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 4 computations (60% saved)

sample556.0ms (63.8%)

Memory

-4.4MiB live, 592.3MiB allocated; 214ms collecting garbage

Samples

410.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-hypot: 153.0ms (98.9% of total)

adjust: 1.0ms (0.6% of total)

Bogosity

preprocess61.0ms (7%)

Memory

-32.4MiB live, 63.8MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	38	19
2	117	19
3	209	19
4	601	19
5	3250	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.9%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 16 to 8 computations (50% saved)

series5.0ms (0.6%)

Memory

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40

Stop Event

1×	iter-limit

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable	Point
1.0ms	x	inf
1.0ms	x	-inf
1.0ms	x	0

rewrite20.0ms (2.3%)

Memory

31.2MiB live, 31.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	19
0	7	15
0	36	12

Stop Event

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

Counts

4 → 28

Calls

Call 1

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

Outputs
(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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(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 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 (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 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
x

eval3.0ms (0.3%)

Memory: 6.4MiB live, 6.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 293 to 78 computations (73.4% saved)

prune8.0ms (0.9%)

Memory

-39.5MiB live, 6.1MiB allocated; 7ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	26	4	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	4	31

Accuracy

100.0%

Counts

31 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
▶	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.3%	#s(approx (sqrt (+ (* x x) (* x x))) (.f64 #s(literal -1 binary64) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 37 to 24 computations (35.1% 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	19	42

Stop Event

1×	iter-limit

Counts

12 → 5

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.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 (* 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
2.0ms	x	inf
2.0ms	x	0
2.0ms	x	-inf

rewrite19.0ms (2.1%)

Memory

16.5MiB live, 16.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	21	45
0	72	45

Stop Event

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

Counts

12 → 58

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (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 (+ (* x x) (* x x))) (*.f64 (sqrt.f64 #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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(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 (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 (+.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)
(*.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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)

eval4.0ms (0.5%)

Memory: 6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 526 to 128 computations (75.7% saved)

prune3.0ms (0.3%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	46	5	51

Accuracy

100.0%

Counts

51 → 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)))
✓	55.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	2.3%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 43 to 28 computations (34.9% saved)

series60.0ms (6.9%)

Memory

-33.8MiB live, 13.6MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	124

Stop Event

1×	iter-limit

Counts

10 → 12

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.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 (* (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 (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
55.0ms	x	-inf
2.0ms	x	0
1.0ms	x	inf

rewrite18.0ms (2.1%)

Memory

18.2MiB live, 18.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
0	20	40
0	71	34

Stop Event

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

Counts

10 → 37

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) (*.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 (+.f64 x x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (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 (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) (fabs.f64 x))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (fabs.f64 x))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(pow.f64 (+.f64 x x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x x))
(fabs.f64 (sqrt.f64 (+.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 (0.3%)

Memory: 4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 417 to 122 computations (70.7% saved)

prune2.0ms (0.3%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	37	6	43

Accuracy

100.0%

Counts

43 → 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)))
▶	99.4%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
✓	55.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	2.3%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 57 to 38 computations (33.3% saved)

series5.0ms (0.6%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	124

Stop Event

1×	iter-limit

Counts

8 → 12

Calls

Call 1

Inputs
(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x x)) (*.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x))))
(*.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) 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 (+ 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 (sqrt (/ 2 x)) (/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) x)) x))
#s(approx (/ 2 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 (/ 2 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
1.0ms	x	-inf
1.0ms	x	inf
1.0ms	x	0

rewrite24.0ms (2.8%)

Memory

-22.0MiB live, 23.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
0	15	42
0	50	42

Stop Event

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

Counts

8 → 18

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 1.6MiB live, 1.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 381 to 100 computations (73.8% saved)

prune2.0ms (0.2%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	23	6	29

Accuracy

100.0%

Counts

29 → 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)))
✓	99.4%	(.f64 (sqrt.f64 x) #s(approx (sqrt (+ x x)) (.f64 x (sqrt.f64 (/.f64 #s(literal 2 binary64) x)))))
✓	55.0%	(sqrt.f64 (*.f64 x (+.f64 x x)))
✓	99.3%	#s(approx (sqrt (+ (* x x) (* x x))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	2.3%	#s(approx (sqrt (+ (* x x) (* x x))) (neg.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))

Compiler

Compiled 57 to 38 computations (33.3% saved)

regimes42.0ms (4.9%)

Memory

-14.8MiB live, 36.1MiB allocated; 7ms collecting garbage

Accuracy

Total -62.1b remaining (-7673.9%)

Threshold costs -62.1b (-7673.9%)

Counts

4 → 1

7 → 1

8 → 1

Calls

Call 1

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

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

Call 2

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

Outputs
(hypot.f64 x x)

Calls

12 calls:

17.0ms	x
3.0ms	x
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
2.0ms	(+.f64 (.f64 x x) (.f64 x x))

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 x x)`
99.3%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.3%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.3%	1	`x`
99.5%	1	`(*.f64 x x)`
99.5%	1	`(+.f64 (.f64 x x) (.f64 x x))`
99.5%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
99.5%	1	`x`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`x`

Compiler

Compiled 137 to 61 computations (55.5% saved)

derivations3.0ms (0.3%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 23 to 13 computations (43.5% saved)

preprocess25.0ms (2.9%)

Memory: -3.2MiB live, 43.0MiB allocated; 3ms collecting garbage
Compiler: Compiled 77 to 47 computations (39% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample556.0ms (63.8%)

preprocess61.0ms (7%)

series5.0ms (0.6%)

rewrite20.0ms (2.3%)

eval3.0ms (0.3%)

prune8.0ms (0.9%)

series6.0ms (0.7%)

rewrite19.0ms (2.1%)

eval4.0ms (0.5%)

prune3.0ms (0.3%)

series60.0ms (6.9%)

rewrite18.0ms (2.1%)

eval3.0ms (0.3%)

prune2.0ms (0.3%)

series5.0ms (0.6%)

rewrite24.0ms (2.8%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

regimes42.0ms (4.9%)

derivations3.0ms (0.3%)

preprocess25.0ms (2.9%)

end0.0ms (0%)

Profiling