Metrics for sqrt sqr

start0.0ms (0%)

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

analyze2.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB 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 (84%)

Memory

5.2MiB live, 1 630.8MiB allocated; 375ms collecting garbage

Samples

811.0ms	4 139×	2	valid
375.0ms	4 117×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 907.0ms

ival-div!: 338.0ms (37.3% of total)

ival-mult!: 222.0ms (24.5% of total)

adjust: 168.0ms (18.5% of total)

ival-sqrt: 139.0ms (15.3% of total)

ival-sub!: 40.0ms (4.4% of total)

Bogosity

preprocess92.0ms (5.2%)

Memory

-34.0MiB live, 56.6MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	71	19
2	159	18
3	389	18
4	1807	18
5	6801	18

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.6%	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Compiler

Compiled 16 to 16 computations (0% saved)

series3.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

8 → 10

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(hole binary64 0))
#s(approx (/ x x) #s(hole binary64 1))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ 1 x) (sqrt (* x x))) #s(hole binary64 1))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (sqrt (* x x)) #s(hole binary64 x))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(hole binary64 2))
#s(approx (* (/ 1 x) (sqrt (* x x))) #s(hole binary64 -1))
#s(approx (sqrt (* x x)) #s(hole binary64 (* -1 x)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))
1.0ms	x	@	0	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))
1.0ms	x	@	inf	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))

Time

Variable

Point

Expression

1.0ms

-inf

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))

1.0ms

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))

1.0ms

inf

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) (/ x x) x (* (/ 1 x) (sqrt (* x x))) (/ 1 x) 1 (sqrt (* x x)) (* x x))

rewrite73.0ms (4.1%)

Memory

10.5MiB live, 107.3MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	119
0	38	78
1	98	51
0	591	51

Stop Event

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

Counts

18 → 51

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)
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(hole binary64 0))
#s(approx (/ x x) #s(hole binary64 1))
#s(approx x #s(hole binary64 x))
#s(approx (* (/ 1 x) (sqrt (* x x))) #s(hole binary64 1))
#s(approx (/ 1 x) #s(hole binary64 (/ 1 x)))
#s(approx (sqrt (* x x)) #s(hole binary64 x))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(hole binary64 2))
#s(approx (* (/ 1 x) (sqrt (* x x))) #s(hole binary64 -1))
#s(approx (sqrt (* x x)) #s(hole binary64 (* -1 x)))

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

eval4.0ms (0.2%)

Memory: 10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 272 to 192 computations (29.4% saved)

prune2.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	2	48

Accuracy

100.0%

Counts

48 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
▶	48.9%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 20 to 20 computations (0% saved)

series0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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(hole binary64 0))
#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(hole binary64 2))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)
0.0ms	x	@	inf	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)
0.0ms	x	@	-inf	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

Time

Variable

Point

Expression

0.0ms

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

0.0ms

inf

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

0.0ms

-inf

((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

rewrite52.0ms (2.9%)

Memory

-25.5MiB live, 65.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	58
0	12	42
1	62	14
0	486	14

Stop Event

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

Counts

6 → 6

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

Outputs
#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)
#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))

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0.1%)

Memory

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

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
✓	48.9%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 45 to 39 computations (13.3% saved)

regimes3.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

2 calls:

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

Results

Accuracy	Segments	Branch
88.6%	2	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
100.0%	2	`x`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes2.0ms (0.1%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

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))

Calls

2 calls:

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
48.9%	1	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
48.9%	1	`x`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch26.0ms (1.5%)

Memory

-2.4MiB live, 53.3MiB allocated; 5ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
24.0ms	-2.9633610220553177e-294	2.4971463291018225e-307

Samples

7.0ms	64×	2	valid
5.0ms	96×	0	valid

Compiler

Compiled 215 to 232 computations (-7.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

adjust: 2.0ms (23.1% of total)

ival-div!: 2.0ms (23.1% of total)

ival-sqrt: 2.0ms (23.1% of total)

ival-mult!: 2.0ms (23.1% of total)

ival-sub!: 1.0ms (11.5% of total)

derivations3.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 21 to 15 computations (28.6% saved)

preprocess20.0ms (1.1%)

Memory: -5.8MiB live, 36.8MiB allocated; 8ms collecting garbage
Compiler: Compiled 29 to 23 computations (20.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0.1%)

sample1.5s (84%)

preprocess92.0ms (5.2%)

series3.0ms (0.2%)

rewrite73.0ms (4.1%)

eval4.0ms (0.2%)

prune2.0ms (0.1%)

series0.0ms (0%)

rewrite52.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes3.0ms (0.2%)

regimes2.0ms (0.1%)

bsearch26.0ms (1.5%)

derivations3.0ms (0.2%)

preprocess20.0ms (1.1%)

end0.0ms (0%)

Profiling