Metrics for 2atan (example 3.5)

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	8.1%	91.9%	0%	0%	0%	0
0%	0%	8.1%	91.9%	0%	0%	0%	1
50%	4.1%	4.1%	91.9%	0%	0%	0%	2
75%	6.1%	2%	91.9%	0%	0%	0%	3
87.5%	7.1%	1%	91.9%	0%	0%	0%	4
93.8%	7.6%	0.5%	91.9%	0%	0%	0%	5
96.9%	7.9%	0.3%	91.9%	0%	0%	0%	6
98.4%	8%	0.1%	91.9%	0%	0%	0%	7
99.2%	8%	0.1%	91.9%	0%	0%	0%	8
99.6%	8.1%	0%	91.9%	0%	0%	0%	9
99.8%	8.1%	0%	91.9%	0%	0%	0%	10
99.9%	8.1%	0%	91.9%	0%	0%	0%	11
100%	8.1%	0%	91.9%	0%	0%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.2s (71%)

Memory

25.4MiB live, 821.4MiB allocated; 259ms collecting garbage

Samples

773.0ms	7 219×	1	valid
120.0ms	831×	2	valid
9.0ms	206×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 685.0ms

ival-atan: 334.0ms (48.7% of total)

adjust: 258.0ms (37.7% of total)

ival-sub!: 48.0ms (7% of total)

ival-add!: 46.0ms (6.7% of total)

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

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

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

Bogosity

preprocess59.0ms (3.4%)

Memory

-5.3MiB live, 40.7MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	37	22
2	115	21
3	332	21
4	1781	21

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.9%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 12 to 12 computations (0% saved)

series2.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Counts

6 → 9

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
N
#s(literal 1 binary64)
(atan.f64 N)

Outputs
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (+ 1 N)) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (+ 1 N))))
#s(approx (+ N 1) #s(hole binary64 1))
#s(approx (+ N 1) #s(hole binary64 (+ 1 N)))
#s(approx N #s(hole binary64 N))
#s(approx (atan N) #s(hole binary64 (atan N)))
#s(approx (+ N 1) #s(hole binary64 (* N (+ 1 (/ 1 N)))))
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (- 1 (* -1 N))) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (- 1 (* -1 N)))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) N 1 (atan N))
0.0ms	N	@	inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) N 1 (atan N))
0.0ms	N	@	0	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) N 1 (atan N))

rewrite199.0ms (11.6%)

Memory

-1.7MiB live, 188.4MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	101
0	35	93
1	179	93
2	690	93
3	3838	93

Stop Event

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

Counts

15 → 15

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
N
#s(literal 1 binary64)
(atan.f64 N)
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (+ 1 N)) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (+ 1 N))))
#s(approx (+ N 1) #s(hole binary64 1))
#s(approx (+ N 1) #s(hole binary64 (+ 1 N)))
#s(approx N #s(hole binary64 N))
#s(approx (atan N) #s(hole binary64 (atan N)))
#s(approx (+ N 1) #s(hole binary64 (* N (+ 1 (/ 1 N)))))
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (- 1 (* -1 N))) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (- 1 (* -1 N)))))

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
N
#s(literal 1 binary64)
(atan.f64 N)
#s(approx (- (atan (+ N 1)) (atan N)) (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)))
#s(approx (atan (+ N 1)) (atan.f64 (+.f64 N #s(literal 1 binary64))))
#s(approx (+ N 1) #s(literal 1 binary64))
#s(approx (+ N 1) (+.f64 N #s(literal 1 binary64)))
#s(approx N N)
#s(approx (atan N) (atan.f64 N))
#s(approx (+ N 1) (+.f64 N #s(literal 1 binary64)))
#s(approx (- (atan (+ N 1)) (atan N)) (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)))
#s(approx (atan (+ N 1)) (atan.f64 (+.f64 N #s(literal 1 binary64))))

eval1.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 40 to 27 computations (32.5% saved)

prune1.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	5	1	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	5	2	7

Accuracy

7.9%

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.9%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
▶	2.0%	(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 14 to 14 computations (0% saved)

series1.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

Counts

6 → 9

Calls

Call 1

Inputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 #s(approx (+ N 1) #s(literal 1 binary64)))
#s(approx (+ N 1) #s(literal 1 binary64))
#s(literal 1 binary64)
(atan.f64 N)
N

Outputs
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (+ 1 N)) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (+ 1 N))))
#s(approx (+ N 1) #s(hole binary64 1))
#s(approx (+ N 1) #s(hole binary64 (+ 1 N)))
#s(approx (atan N) #s(hole binary64 (atan N)))
#s(approx N #s(hole binary64 N))
#s(approx (+ N 1) #s(hole binary64 (* N (+ 1 (/ 1 N)))))
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (- 1 (* -1 N))) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (- 1 (* -1 N)))))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) 1 (atan N) N)
0.0ms	N	@	inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) 1 (atan N) N)
0.0ms	N	@	0	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) 1 (atan N) N)

rewrite183.0ms (10.7%)

Memory

1.5MiB live, 132.5MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	107
0	33	99
1	195	99
2	805	99
3	4544	99

Stop Event

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

Counts

15 → 9

Calls

Call 1

Inputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 #s(approx (+ N 1) #s(literal 1 binary64)))
#s(approx (+ N 1) #s(literal 1 binary64))
#s(literal 1 binary64)
(atan.f64 N)
N
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (+ 1 N)) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (+ 1 N))))
#s(approx (+ N 1) #s(hole binary64 1))
#s(approx (+ N 1) #s(hole binary64 (+ 1 N)))
#s(approx (atan N) #s(hole binary64 (atan N)))
#s(approx N #s(hole binary64 N))
#s(approx (+ N 1) #s(hole binary64 (* N (+ 1 (/ 1 N)))))
#s(approx (- (atan (+ N 1)) (atan N)) #s(hole binary64 (- (atan (- 1 (* -1 N))) (atan N))))
#s(approx (atan (+ N 1)) #s(hole binary64 (atan (- 1 (* -1 N)))))

Outputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 #s(approx (+ N 1) #s(literal 1 binary64)))
#s(approx (+ N 1) #s(literal 1 binary64))
#s(literal 1 binary64)
(atan.f64 N)
N
#s(approx (+ N 1) #s(literal 1 binary64))
#s(approx (atan N) (atan.f64 N))
#s(approx N N)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 13 to 13 computations (0% saved)

prune1.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	2	0	2
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	2	2	4

Accuracy

7.9%

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.9%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
✓	2.0%	(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 25 to 25 computations (0% saved)

regimes3.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Calls

2 calls:

1.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
7.9%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
7.9%	1	`N`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes2.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))

Outputs
(-.f64 (atan.f64 #s(approx (+ N 1) #s(literal 1 binary64))) (atan.f64 N))

Calls

2 calls:

1.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
2.0%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
2.0%	1	`N`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations15.0ms (0.9%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 11 to 11 computations (0% saved)

preprocess30.0ms (1.7%)

Memory: -21.2MiB live, 26.4MiB allocated; 7ms collecting garbage
Compiler: Compiled 33 to 29 computations (12.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample1.2s (71%)

preprocess59.0ms (3.4%)

series2.0ms (0.1%)

rewrite199.0ms (11.6%)

eval1.0ms (0%)

prune1.0ms (0.1%)

series1.0ms (0.1%)

rewrite183.0ms (10.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes3.0ms (0.2%)

regimes2.0ms (0.1%)

derivations15.0ms (0.9%)

preprocess30.0ms (1.7%)

end0.0ms (0%)

Profiling