Metrics for sqrt sqr

start0.0ms (0%)

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

analyze4.0ms (0.2%)

Memory

-46.0MiB live, 2.7MiB allocated; 5ms 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 (80%)

Memory

73.3MiB live, 1 961.6MiB allocated; 370ms collecting garbage

Samples

800.0ms	4 155×	2	valid
290.0ms	4 101×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 886.0ms

ival-div!: 250.0ms (28.2% of total)

ival-sqrt: 224.0ms (25.3% of total)

ival-mult!: 201.0ms (22.7% of total)

adjust: 168.0ms (19% of total)

ival-sub!: 43.0ms (4.9% of total)

Bogosity

explain169.0ms (9.3%)

Memory

-37.1MiB live, 206.1MiB allocated; 83ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
118	-	4	(1.3425959349544588e-159)	`(sqrt.f64 (*.f64 x x))`
0	-	0	-	`(/.f64 #s(literal 1 binary64) x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
0	-	0	-	`(/.f64 x x)`
0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x)))`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 x x))`	oflow-rescue	66	0
↳	`(*.f64 x x)`	overflow	66
`sqrt.f64`	`(sqrt.f64 (*.f64 x x))`	uflow-rescue	48	0
↳	`(*.f64 x x)`	underflow	48

Confusion

	Predicted +	Predicted -
+	114	16
-	0	126

Precision

1.0

Recall

0.8769230769230769

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	114	0	16
-	0	0	126

Precision?

1.0

Recall?

0.8769230769230769

Freqs

test

number	freq
0	142
1	114

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

63.0ms	234×	0	valid
38.0ms	278×	2	valid

Compiler

Compiled 86 to 28 computations (67.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-mult!: 58.0ms (69.9% of total)

ival-div!: 8.0ms (9.6% of total)

adjust: 7.0ms (8.4% of total)

ival-sqrt: 7.0ms (8.4% of total)

ival-sub!: 3.0ms (3.6% of total)

preprocess44.0ms (2.4%)

Memory

-1.7MiB live, 43.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	57	19
2	128	18
3	334	18
4	1715	18
5	6366	18

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.8%	(-.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)

series3.0ms (0.2%)

Memory

5.6MiB live, 5.6MiB 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))

rewrite58.0ms (3.2%)

Memory

30.5MiB live, 77.3MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	119
0	34	78
1	89	51
0	504	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)
(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 (pow.f64 x #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 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) (pow.f64 x #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
#s(literal 1 binary64)
x
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.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))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.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 (sqrt.f64 x) (.f64 (sqrt.f64 x) x))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 x)))
(*.f64 (pow.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64)))
(.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 x x)
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(fabs.f64 (pow.f64 x #s(literal 2 binary64)))
(neg.f64 (*.f64 x (neg.f64 x)))
(neg.f64 (*.f64 (neg.f64 x) x))
#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) (pow.f64 x #s(literal -1 binary64)))
#s(approx (sqrt (* x x)) 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)) (neg.f64 x))

eval8.0ms (0.5%)

Memory: -31.7MiB live, 14.0MiB allocated; 5ms collecting garbage
Compiler: Compiled 771 to 193 computations (75% saved)

prune1.0ms (0.1%)

Memory

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

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	2	55

Accuracy

100.0%

Counts

55 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.4%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
▶	55.7%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 28 to 20 computations (28.6% saved)

series0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

rewrite31.0ms (1.7%)

Memory

-5.2MiB live, 41.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	58
0	12	42
1	56	14
0	407	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: 0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 56 to 12 computations (78.6% saved)

prune3.0ms (0.2%)

Memory

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

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	4	2	6

Accuracy

100.0%

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	47.4%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
✓	55.7%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 68 to 39 computations (42.6% saved)

regimes3.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB 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:

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
92.4%	2	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
100.0%	2	`x`

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes2.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB 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
55.7%	1	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
55.7%	1	`x`

Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch24.0ms (1.3%)

Memory

-11.5MiB live, 34.7MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	-5.4221267884759476e-294	2.2464074912194927e-304

Samples

11.0ms	96×	2	valid
3.0ms	64×	0	valid

Compiler

Compiled 295 to 232 computations (21.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-div!: 3.0ms (28.7% of total)

ival-mult!: 3.0ms (28.7% of total)

adjust: 2.0ms (19.1% of total)

ival-sqrt: 2.0ms (19.1% of total)

ival-sub!: 1.0ms (9.6% of total)

derivations1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 46 to 15 computations (67.4% saved)

preprocess14.0ms (0.8%)

Memory: 26.9MiB live, 26.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 128 to 56 computations (56.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze4.0ms (0.2%)

sample1.5s (80%)

explain169.0ms (9.3%)

preprocess44.0ms (2.4%)

series3.0ms (0.2%)

rewrite58.0ms (3.2%)

eval8.0ms (0.5%)

prune1.0ms (0.1%)

series0.0ms (0%)

rewrite31.0ms (1.7%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes3.0ms (0.2%)

regimes2.0ms (0.1%)

bsearch24.0ms (1.3%)

derivations1.0ms (0%)

preprocess14.0ms (0.8%)

end0.0ms (0%)

Profiling