Metrics for pow(2, x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample759.0ms (65.3%)

Memory

81.5MiB live, 404.8MiB allocated

Samples

408.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 233.0ms

ival-pow: 140.0ms (60.1% of total)

ival-<=: 61.0ms (26.2% of total)

exact: 16.0ms (6.9% of total)

ival-and: 11.0ms (4.7% of total)

ival-assert: 5.0ms (2.1% of total)

Bogosity

explain35.0ms (3%)

Memory

14.0MiB live, 14.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 2 binary64)`
-	-	`(pow.f64 #s(literal 2 binary64) x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

18.0ms

512×

valid

Compiler

Compiled 17 to 13 computations (23.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-pow: 6.0ms (84.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess13.0ms (1.1%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	11	9
2	15	9
3	18	9
4	22	9
5	29	9
6	36	9
0	3	3
0	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 3 to 3 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 #s(literal 2 binary64) x)

Compiler

Compiled 3 to 3 computations (0% saved)

simplify2.0ms (0.2%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 #s(literal 2 binary64) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize12.0ms (1%)

Memory

4.1MiB live, 4.1MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(pow.f64 #s(literal 2 binary64) x)

Samples

8.0ms

256×

valid

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-pow: 3.0ms (90.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Memory

0.3MiB live, 0.3MiB allocated

Counts

1 → 5

Calls

Call 1

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

Outputs
1
(+ 1 (* x (log 2)))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(pow 2 x)

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((pow 2 x))
0.0ms	x	@	-inf	((pow 2 x))
0.0ms	x	@	inf	((pow 2 x))

simplify39.0ms (3.3%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	49
1	65	49
2	163	47
3	331	47
4	663	47
5	1009	47
6	1059	47
7	1070	47
8	1075	47
9	1076	47
10	1076	47
11	1334	47
12	1343	47
13	1356	47
14	1356	47
0	1356	41

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 5

Calls

Call 1

Inputs
1
(+ 1 (* x (log 2)))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(pow 2 x)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* x (log 2)))
(fma.f64 (log.f64 #s(literal 2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) x #s(literal 1 binary64)) x) (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (*.f64 #s(literal 1/6 binary64) x) (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) x) (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) x) (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow 2 x)
(pow.f64 #s(literal 2 binary64) x)

rewrite70.0ms (6%)

Memory

8.4MiB live, 8.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	3
1	10	3
2	36	3
3	193	3
0	2028	3

Stop Event

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

Counts

1 → 24

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (exp.f64 x) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 x) (/.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 16 binary64) x) (pow.f64 #s(literal 16 binary64) x))
(pow.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) x)
(pow.f64 #s(literal 16 binary64) x)
(pow.f64 #s(literal 8 binary64) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 4 binary64) (neg.f64 x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 2 binary64) (neg.f64 x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 3 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 4 binary64))
(pow.f64 (pow.f64 #s(literal 16 binary64) x) #s(literal 2 binary64))
(pow.f64 (exp.f64 x) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 x) (log.f64 #s(literal 2 binary64)))
(pow.f64 #s(literal 4 binary64) x)
(pow.f64 #s(literal 2 binary64) x)
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 4 binary64) (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) (neg.f64 x)))
(sqrt.f64 (pow.f64 #s(literal 16 binary64) x))
(exp.f64 (*.f64 (log.f64 (exp.f64 x)) (log.f64 #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) x))

eval3.0ms (0.3%)

Memory: 2.4MiB live, 2.4MiB allocated
Compiler: Compiled 192 to 68 computations (64.6% saved)

prune1.0ms (0.1%)

Memory

1.5MiB live, 1.5MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Accuracy

100.0%

Counts

30 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 #s(literal 2 binary64) x)
▶	97.7%	#s(approx (pow 2 x) #s(literal 1 binary64))

Compiler

Compiled 8 to 8 computations (0% saved)

simplify3.0ms (0.2%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (pow 2 x) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
0	5	6
1	7	6
0	7	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
#s(approx (pow 2 x) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
#s(approx (pow 2 x) #s(literal 1 binary64))
#s(literal 1 binary64)

localize43.0ms (3.7%)

Memory

-70.6MiB live, 5.7MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	1.4625120183262466	#s(approx (pow 2 x) #s(literal 1 binary64))

Samples

39.0ms

256×

valid

Compiler

Compiled 6 to 6 computations (0% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 14.0ms (96% of total)

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

exact: 0.0ms (0% of total)

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

series0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Counts

1 → 5

Calls

Call 1

Inputs
#s(approx (pow 2 x) #s(literal 1 binary64))

Outputs
1
(+ 1 (* x (log 2)))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(pow 2 x)

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((pow 2 x))
0.0ms	x	@	inf	((pow 2 x))
0.0ms	x	@	-inf	((pow 2 x))

simplify39.0ms (3.3%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	49
1	65	49
2	163	47
3	331	47
4	676	47
5	1049	47
6	1099	47
7	1110	47
8	1115	47
9	1116	47
10	1116	47
11	1370	47
12	1379	47
13	1392	47
14	1392	47
0	1392	41

Stop Event

1×	iter limit
1×	saturated

Counts

5 → 5

Calls

Call 1

Inputs
1
(+ 1 (* x (log 2)))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(pow 2 x)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* x (log 2)))
(fma.f64 (log.f64 #s(literal 2 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ (log 2) (* 1/2 (* x (pow (log 2) 2))))))
(fma.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) x #s(literal 1 binary64)) x) (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (log 2) (* x (+ (* 1/6 (* x (pow (log 2) 3))) (* 1/2 (pow (log 2) 2)))))))
(fma.f64 (.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (*.f64 (log.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64)) x) (log.f64 #s(literal 2 binary64)) #s(literal 1 binary64))
(pow 2 x)
(pow.f64 #s(literal 2 binary64) x)

rewrite63.0ms (5.4%)

Memory

3.6MiB live, 3.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
0	5	5
1	13	5
2	38	5
3	193	5
0	2030	5

Stop Event

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

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (pow 2 x) #s(literal 1 binary64))

Outputs
#s(approx (pow 2 x) #s(literal 1 binary64))

eval1.0ms (0.1%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 61 to 25 computations (59% saved)

prune1.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	5	0	5
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	5	2	7

Accuracy

100.0%

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 #s(literal 2 binary64) x)
✓	97.7%	#s(approx (pow 2 x) #s(literal 1 binary64))

Compiler

Compiled 16 to 15 computations (6.3% saved)

regimes2.0ms (0.2%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (pow 2 x) #s(literal 1 binary64))
(pow.f64 #s(literal 2 binary64) x)

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 4 to 4 computations (0% saved)

regimes2.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (pow 2 x) #s(literal 1 binary64))

Outputs
#s(approx (pow 2 x) #s(literal 1 binary64))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`(pow.f64 #s(literal 2 binary64) x)`

Compiler

Compiled 4 to 4 computations (0% saved)

simplify9.0ms (0.8%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8

Stop Event

1×

saturated

Calls

Call 1

Inputs
(pow.f64 #s(literal 2 binary64) x)
#s(approx (pow 2 x) #s(literal 1 binary64))

Outputs
(pow.f64 #s(literal 2 binary64) x)
#s(approx (pow 2 x) #s(literal 1 binary64))

soundness48.0ms (4.1%)

Memory

1.1MiB live, 1.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	49
1	65	49
2	163	47
3	331	47
4	663	47
5	1009	47
6	1059	47
7	1070	47
8	1075	47
9	1076	47
10	1076	47
11	1334	47
12	1343	47
13	1356	47
14	1356	47
0	1356	41

Stop Event

1×	done
1×	iter limit
1×	saturated

Compiler

Compiled 9 to 9 computations (0% saved)

preprocess15.0ms (1.3%)

Memory: 10.5MiB live, 10.5MiB allocated
Compiler: Compiled 22 to 20 computations (9.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample759.0ms (65.3%)

explain35.0ms (3%)

preprocess13.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.2%)

localize12.0ms (1%)

series1.0ms (0.1%)

simplify39.0ms (3.3%)

rewrite70.0ms (6%)

eval3.0ms (0.3%)

prune1.0ms (0.1%)

simplify3.0ms (0.2%)

localize43.0ms (3.7%)

series0.0ms (0%)

simplify39.0ms (3.3%)

rewrite63.0ms (5.4%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

regimes2.0ms (0.2%)

regimes2.0ms (0.2%)

simplify9.0ms (0.8%)

soundness48.0ms (4.1%)

preprocess15.0ms (1.3%)

end0.0ms (0%)

Profiling