Metrics for sqrt D (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB 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 8 to 7 computations (12.5% saved)

sample604.0ms (54.8%)

Memory

-3.8MiB live, 384.9MiB allocated; 146ms collecting garbage

Samples

399.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 257.0ms

ival-pow2: 150.0ms (58.3% of total)

ival-mult: 48.0ms (18.7% of total)

ival-sqrt: 48.0ms (18.7% of total)

exact: 6.0ms (2.3% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

explain64.0ms (5.8%)

Memory

8.6MiB live, 53.5MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
133	-	2	(-1.1808629151722166e-160)	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	67	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	underflow	67
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	67
`sqrt.f64`	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	64	0
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`	overflow	64
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	64

Confusion

	Predicted +	Predicted -
+	131	2
-	0	123

Precision

1.0

Recall

0.9849624060150376

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	2
-	0	0	123

Precision?

1.0

Recall?

0.9849624060150376

Freqs

test

number	freq
0	125
1	131

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow2: 6.0ms (46.7% of total)

ival-mult: 3.0ms (23.3% of total)

ival-sqrt: 3.0ms (23.3% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess235.0ms (21.3%)

Memory

-3.0MiB live, 95.6MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	19
2	55	19
3	167	19
4	408	19
5	1304	19
6	5101	19
0	5	6
0	8	6
1	13	6
2	34	6
3	106	6
4	358	6
5	1096	6
6	4530	6
0	8083	3

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.8%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series4.0ms (0.4%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
x

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) 2 (pow x 2) x)
1.0ms	x	@	0	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) 2 (pow x 2) x)
1.0ms	x	@	-inf	((sqrt (* 2 (pow x 2))) (* 2 (pow x 2)) 2 (pow x 2) x)

rewrite35.0ms (3.1%)

Memory

-18.0MiB live, 26.8MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	61
0	21	60
1	42	54
0	138	49

Stop Event

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

Counts

10 → 46

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) x)
(*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)))
(pow.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))
(hypot.f64 (*.f64 #s(literal -1 binary64) x) (exp.f64 (log.f64 x)))
(hypot.f64 (*.f64 #s(literal -1 binary64) x) x)
(hypot.f64 (exp.f64 (log.f64 x)) (*.f64 #s(literal -1 binary64) x))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 x (*.f64 #s(literal -1 binary64) x))
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x x)
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 2 binary64)))
(*.f64 x (+.f64 x x))
(.f64 #s(literal 2 binary64) (.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))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(fma.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 x x (*.f64 x x))
(-.f64 (.f64 x x) (.f64 (*.f64 #s(literal -1 binary64) x) x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
#s(literal 2 binary64)
(.f64 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(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))))
x
#s(approx (sqrt (* 2 (pow x 2))) (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) x))
#s(approx (* 2 (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64)))
#s(approx (pow x 2) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (* 2 (pow x 2))) (.f64 #s(literal -1 binary64) (.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) x)))

eval5.0ms (0.4%)

Memory: 6.5MiB live, 6.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 425 to 113 computations (73.4% saved)

prune6.0ms (0.5%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accuracy

100.0%

Counts

48 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))

Compiler

Compiled 7 to 4 computations (42.9% saved)

series2.0ms (0.2%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Counts

4 → 4

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* -1 x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) (* -1 x) -1 x)

1.0ms

-inf

((sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) (* -1 x) -1 x)

1.0ms

((sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) (* -1 x) -1 x)

rewrite55.0ms (5%)

Memory

-19.6MiB live, 24.6MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	48
0	17	38
1	54	29
0	447	29

Stop Event

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

Counts

8 → 21

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal -1 binary64))) (sqrt.f64 (*.f64 x #s(literal -2 binary64))))
(.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) (fabs.f64 x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (.f64 x x) #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x x) #s(literal 2 binary64)) #s(literal 0 binary64))))
(cosh.f64 (asinh.f64 #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(hypot.f64 (.f64 x #s(literal -1 binary64)) (.f64 x #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(*.f64 x #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) x)
(neg.f64 x)
#s(literal -1 binary64)
x
#s(approx (sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) (*.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))))
#s(approx (* -1 x) (*.f64 x #s(literal -1 binary64)))
#s(approx x x)
#s(approx (sqrt (+ (* (* -1 x) (* -1 x)) (* (* -1 x) (* -1 x)))) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))) x))

eval3.0ms (0.3%)

Memory: 3.5MiB live, 3.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 239 to 65 computations (72.8% saved)

prune4.0ms (0.4%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	1	29

Accuracy

100.0%

Counts

29 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))

Compiler

Compiled 20 to 12 computations (40% saved)

regimes5.0ms (0.5%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))

Outputs
(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(pow.f64 x #s(literal 2 binary64))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`(pow.f64 x #s(literal 2 binary64))`
100.0%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
100.0%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.4%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

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

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
51.8%	1	`(pow.f64 x #s(literal 2 binary64))`
51.8%	1	`(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64)))`
51.8%	1	`(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))`
51.8%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify56.0ms (5.1%)

Memory

-29.0MiB live, 26.9MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	16	11
3	23	11
4	55	11
5	377	11
6	3461	11

Stop Event

1×	node limit

Calls

Call 1

Inputs
(hypot.f64 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 2 binary64))))

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

derivations2.0ms (0.1%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess18.0ms (1.6%)

Memory: 16.0MiB live, 16.0MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 66 to 42 computations (36.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample604.0ms (54.8%)

explain64.0ms (5.8%)

preprocess235.0ms (21.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.4%)

rewrite35.0ms (3.1%)

eval5.0ms (0.4%)

prune6.0ms (0.5%)

series2.0ms (0.2%)

rewrite55.0ms (5%)

eval3.0ms (0.3%)

prune4.0ms (0.4%)

regimes5.0ms (0.5%)

regimes4.0ms (0.4%)

simplify56.0ms (5.1%)

derivations2.0ms (0.1%)

preprocess18.0ms (1.6%)

end0.0ms (0%)

Profiling