Metrics for sqrt sqr

start0.0ms (0%)

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

analyze3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB 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 (68.5%)

Memory

39.4MiB live, 1 385.2MiB allocated; 861ms collecting garbage

Samples

851.0ms	4 132×	2	valid
329.0ms	4 124×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 669.0ms

ival-div!: 263.0ms (39.3% of total)

ival-mult!: 148.0ms (22.1% of total)

ival-sqrt: 113.0ms (16.9% of total)

adjust: 104.0ms (15.5% of total)

ival-sub!: 40.0ms (6% of total)

Bogosity

explain133.0ms (5.9%)

Memory

-35.3MiB live, 273.1MiB allocated; 60ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	6	(5.1479642094650075e-161)	`(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	65	0
↳	`(*.f64 x x)`	overflow	65
`sqrt.f64`	`(sqrt.f64 (*.f64 x x))`	uflow-rescue	54	0
↳	`(*.f64 x x)`	underflow	54

Confusion

	Predicted +	Predicted -
+	119	14
-	0	123

Precision

1.0

Recall

0.8947368421052632

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	119	0	14
-	0	0	123

Precision?

1.0

Recall?

0.8947368421052632

Freqs

test

number	freq
0	137
1	119

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms	246×	2	valid
15.0ms	266×	0	valid

Compiler

Compiled 86 to 28 computations (67.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

adjust: 9.0ms (25.7% of total)

ival-div!: 9.0ms (25.7% of total)

ival-mult!: 8.0ms (22.9% of total)

ival-sqrt: 7.0ms (20% of total)

ival-sub!: 2.0ms (5.7% of total)

preprocess173.0ms (7.7%)

Memory

28.6MiB live, 168.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	61	19
2	132	18
3	337	18
4	1715	18
5	6496	18
0	8	12
0	14	8
1	30	6
2	64	6
3	184	6
4	1061	6
5	6955	6
0	8061	6

Stop Event

1×	iter-limit
1×	node-limit
1×	iter-limit
1×	node-limit

Calls

Call 1

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

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

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

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 12 to 8 computations (33.3% saved)

series25.0ms (1.1%)

Memory

-26.3MiB live, 20.9MiB allocated; 11ms 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
23.0ms	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

23.0ms

-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))

rewrite67.0ms (3%)

Memory

32.9MiB live, 76.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	119
0	38	78
1	94	51
0	541	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) (pow.f64 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 (*.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) (pow.f64 x #s(literal -1 binary64)))
#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))

eval13.0ms (0.6%)

Memory: -28.7MiB live, 15.3MiB allocated; 10ms collecting garbage
Compiler: Compiled 771 to 193 computations (75% saved)

prune3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB 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
▶	53.5%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
▶	49.7%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 28 to 20 computations (28.6% saved)

series1.0ms (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	@	-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)
0.0ms	x	@	0	((- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 0 (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) 2)

Time

Variable

Point

Expression

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)

0.0ms

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

rewrite91.0ms (4%)

Memory

-10.4MiB live, 85.9MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	58
0	12	42
1	58	14
0	438	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))

eval1.0ms (0%)

Memory: 1.4MiB live, 1.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 56 to 12 computations (78.6% saved)

prune2.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB 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
✓	53.5%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 2 binary64))
✓	49.7%	#s(approx (- (/ x x) (* (/ 1 x) (sqrt (* x x)))) #s(literal 0 binary64))

Compiler

Compiled 68 to 39 computations (42.6% saved)

regimes6.0ms (0.3%)

Memory

10.3MiB live, 10.3MiB 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:

3.0ms	x
2.0ms	(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))

Results

Accuracy	Segments	Branch
91.7%	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)

regimes4.0ms (0.2%)

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:

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
49.7%	1	`(-.f64 (/.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 (.f64 x x))))`
49.7%	1	`x`

Compiler

Compiled 13 to 9 computations (30.8% saved)

bsearch72.0ms (3.2%)

Memory

7.8MiB live, 56.2MiB allocated; 3ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
67.0ms	-3.0712506694547646e-296	5.033116835688714e-287

Samples

17.0ms	80×	2	valid
9.0ms	96×	0	valid

Compiler

Compiled 323 to 254 computations (21.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-div!: 5.0ms (26.7% of total)

ival-mult!: 5.0ms (26.7% of total)

ival-sqrt: 4.0ms (21.3% of total)

adjust: 3.0ms (16% of total)

ival-sub!: 2.0ms (10.7% of total)

derivations4.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 46 to 15 computations (67.4% saved)

preprocess112.0ms (5%)

Memory: 3.0MiB live, 49.8MiB allocated; 3ms 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%)

analyze3.0ms (0.1%)

sample1.5s (68.5%)

explain133.0ms (5.9%)

preprocess173.0ms (7.7%)

eval0.0ms (0%)

prune0.0ms (0%)

series25.0ms (1.1%)

rewrite67.0ms (3%)

eval13.0ms (0.6%)

prune3.0ms (0.1%)

series1.0ms (0%)

rewrite91.0ms (4%)

eval1.0ms (0%)

prune2.0ms (0.1%)

regimes6.0ms (0.3%)

regimes4.0ms (0.2%)

bsearch72.0ms (3.2%)

derivations4.0ms (0.2%)

preprocess112.0ms (5%)

end0.0ms (0%)

Profiling