Metrics for sqrt sqr

start0.0ms (0%)

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

analyze2.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.5s (73.1%)

Memory

39.3MiB live, 1 101.3MiB allocated; 1.1s collecting garbage

Samples

651.0ms	4 080×	2	valid
514.0ms	4 176×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 582.0ms

ival-mult!: 147.0ms (25.3% of total)

ival-sqrt: 143.0ms (24.6% of total)

ival-div!: 136.0ms (23.4% of total)

adjust: 110.0ms (18.9% of total)

ival-sub!: 46.0ms (7.9% of total)

Bogosity

preprocess69.0ms (3.3%)

Memory

-1.4MiB live, 43.6MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	87	19
2	386	15
3	3509	15

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Compiler

Compiled 24 to 16 computations (33.3% saved)

series67.0ms (3.2%)

Memory

-25.9MiB live, 27.3MiB allocated; 19ms collecting garbage

Counts

8 → 8

Calls

Call 1

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

Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(approx (/ x x) #s(literal 1 binary64))
#s(approx x x)
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx (* x x) (pow.f64 x #s(literal 2 binary64)))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(approx (* (/ 1 x) (sqrt (* x x))) #s(literal -1 binary64))
#s(approx (sqrt (* x x)) (*.f64 #s(literal -1 binary64) x))

Calls

3 calls:

Time	Variable	Point
2.0ms	x	-inf
2.0ms	x	0
1.0ms	x	inf

rewrite130.0ms (6.3%)

Memory

-0.0MiB live, 89.1MiB allocated; 27ms collecting garbage

Counts

8 → 34

Calls

Call 1

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

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

eval6.0ms (0.3%)

Memory: 5.5MiB live, 5.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 388 to 97 computations (75% saved)

prune2.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Accuracy

100.0%

Counts

32 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.9%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
▶	46.3%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 28 to 20 computations (28.6% saved)

series74.0ms (3.6%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))

Calls

3 calls:

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

rewrite148.0ms (7.1%)

Memory

15.3MiB live, 61.2MiB allocated; 8ms collecting garbage

Counts

4 → 7

Calls

Call 1

Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
#s(approx (- 1 (* (/ 1 x) (fabs x))) #s(literal 0 binary64))
#s(literal 0 binary64)
(sinh.f64 #s(literal 0 binary64))
#s(approx (- 1 (* (/ 1 x) (fabs x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 x (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))

eval1.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 70 to 23 computations (67.1% saved)

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	5	0	5
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	5	2	7

Accuracy

100.0%

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.9%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
✓	46.3%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes7.0ms (0.3%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

3 → 2

Calls

Call 1

Inputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Call 2

Inputs

#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))

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

Outputs
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Calls

4 calls:

2.0ms	x
1.0ms	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))
1.0ms	x
1.0ms	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Results

Accuracy	Segments	Branch
46.3%	1	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
46.3%	1	`x`
90.5%	2	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
100.0%	2	`x`

Compiler

Compiled 66 to 37 computations (43.9% saved)

bsearch36.0ms (1.7%)

Memory

-47.2MiB live, 8.6MiB allocated; 20ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
33.0ms	-1.0360770444954654e-300	3.0037737357008347e-307

Samples

20.0ms	80×	0	valid
8.0ms	64×	2	valid

Compiler

Compiled 267 to 210 computations (21.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 18.0ms (74.4% of total)

adjust: 2.0ms (8.3% of total)

ival-div!: 2.0ms (8.3% of total)

ival-mult!: 2.0ms (8.3% of total)

ival-sub!: 1.0ms (4.1% of total)

derivations0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 46 to 15 computations (67.4% saved)

preprocess14.0ms (0.7%)

Memory: 13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 58 to 23 computations (60.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0.1%)

sample1.5s (73.1%)

preprocess69.0ms (3.3%)

series67.0ms (3.2%)

rewrite130.0ms (6.3%)

eval6.0ms (0.3%)

prune2.0ms (0.1%)

series74.0ms (3.6%)

rewrite148.0ms (7.1%)

eval1.0ms (0%)

prune1.0ms (0%)

regimes7.0ms (0.3%)

bsearch36.0ms (1.7%)

derivations0.0ms (0%)

preprocess14.0ms (0.7%)

end0.0ms (0%)

Profiling