Details

sample286.0ms

Algorithm

intervals

Results

75.0ms	100×	body	1280	valid
52.0ms	170×	body	80	valid
34.0ms	43×	body	10240	exit
29.0ms	51×	body	640	valid
11.0ms	171×	body	80	nan
11.0ms	29×	body	320	valid
10.0ms	15×	body	640	nan
9.0ms	14×	body	1280	nan
4.0ms	12×	body	320	nan
3.0ms	14×	body	160	valid
1.0ms	6×	body	160	nan

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
6	2902
5	690
4	225
3	81
2	34
1	17
0	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
14×	`unpow-prod-down`
13×	`pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `div-inv` `flip--`

Counts

2 → 54

Calls

2 calls:

16.0ms	(pow (+ x 1.0) (/ 1.0 n))
133.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series821.0ms

Counts

2 → 6

Calls

2 calls:

259.0ms	(pow (+ x 1.0) (/ 1.0 n))
562.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify5.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	3380
2	1040
1	396
0	150

prune835.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (cbrt (* (* (pow (+ x 1.0) (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
36×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`times-frac`
13×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

23.0ms	(pow (+ x 1.0) (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
23.0ms	(pow (+ x 1.0) (/ 1.0 n))
96.0ms	(- (cbrt (* (* (pow (+ x 1.0) (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

317.0ms	(pow (+ x 1.0) (/ 1.0 n))
241.0ms	(pow (+ x 1.0) (/ 1.0 n))
252.0ms	(pow (+ x 1.0) (/ 1.0 n))
553.0ms	(- (cbrt (* (* (pow (+ x 1.0) (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify5.4s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	3334
2	1001
1	378
0	142

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.5b

localize109.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(- (cbrt (* (* (posit16->real (real->posit16 (pow (+ x 1.0) (/ 1.0 n)))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
36×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
27×	`times-frac`
13×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `insert-posit16` `sqr-pow`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 104

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
24.0ms	(pow (+ x 1.0) (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
46.0ms	(- (cbrt (* (* (posit16->real (real->posit16 (pow (+ x 1.0) (/ 1.0 n)))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

297.0ms	(pow (+ x 1.0) (/ 1.0 n))
266.0ms	(pow (+ x 1.0) (/ 1.0 n))
255.0ms	(pow (+ x 1.0) (/ 1.0 n))
473.0ms	(- (cbrt (* (* (posit16->real (real->posit16 (pow (+ x 1.0) (/ 1.0 n)))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify4.9s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	3208
2	1027
1	389
0	145

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.5b

localize157.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n))))
2.4b	(- (cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
32.9b	(posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n)))))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`pow-unpow`
12×	`add-cube-cbrt`
9×	`times-frac`
6×	`add-log-exp`
5×	`pow1` `unpow-prod-down` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16`
3×	`difference-of-squares`
2×	`sqr-pow`
1×	`cbrt-prod` `pow-to-exp` `sub-neg` `pow-pow` `flip3--` `pow1/3` `diff-log` `pow-exp` `div-inv` `remove-posit16` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

30.0ms	(pow (+ x 1.0) (/ 1.0 n))
119.0ms	(cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n))))
62.0ms	(- (cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
1.0ms	(posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

246.0ms	(pow (+ x 1.0) (/ 1.0 n))
545.0ms	(cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n))))
713.0ms	(- (cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
78.0ms	(posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n)))))

simplify4.0s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1503
1	539
0	206

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.2b

regimes959.0ms

Accuracy

83.2% (1.5b remaining)

Error of 22.0b against oracle of 20.5b and baseline of 29.5b

bsearch355.0ms

Steps

Iters	Range		Point
10	0.00018705152818348546	24130438545.104744	33522299.50529173
8	-351300497490.8783	-26711381.42537418	-74876590.12174678

simplify14.0ms

Iterations

Iter	Nodes
done	41
1	41
0	30

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.6s	3175×	body	1280	valid
926.0ms	1569×	body	640	valid
856.0ms	1179×	body	10240	exit
791.0ms	5178×	body	80	nan
544.0ms	626×	body	1280	nan
483.0ms	4651×	body	80	valid
434.0ms	631×	body	640	nan
380.0ms	166×	body	160	nan
362.0ms	846×	body	320	valid
106.0ms	354×	body	320	nan
97.0ms	443×	body	160	valid