Details

sample231.0ms

Algorithm

intervals

Results

79.0ms	100×	body	1280	valid
32.0ms	43×	body	10240	exit
31.0ms	51×	body	640	valid
16.0ms	170×	body	80	valid
12.0ms	29×	body	320	valid
12.0ms	171×	body	80	nan
9.0ms	14×	body	1280	nan
9.0ms	15×	body	640	nan
4.0ms	12×	body	320	nan
3.0ms	14×	body	160	valid
2.0ms	6×	body	160	nan

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1169
4	263
3	84
2	36
1	19
0	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1) (/ 1 n))
1.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite109.0ms

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:

18.0ms	(pow (+ x 1) (/ 1 n))
90.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series301.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(pow (+ x 1) (/ 1 n))
212.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify1.8s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	2507
2	827
1	348
0	136

prune313.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
1.3b	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

rewrite98.0ms

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:

11.0ms	(pow (+ x 1) (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
14.0ms	(pow (+ x 1) (/ 1 n))
58.0ms	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(pow (+ x 1) (/ 1 n))
114.0ms	(pow (+ x 1) (/ 1 n))
86.0ms	(pow (+ x 1) (/ 1 n))
212.0ms	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

simplify1.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
3	2485
2	838
1	331
0	128

prune535.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
2.6b	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) 1)) (pow x (/ 1 n)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`unpow-prod-down`
28×	`add-cube-cbrt`
26×	`pow-unpow`
18×	`times-frac` `add-exp-log`
13×	`sqr-pow`
10×	`swap-sqr`
9×	`prod-exp` `unswap-sqr`
8×	`pow-to-exp` `associate-r` `associate-l` `pow-exp` `distribute-lft-out`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
4×	`insert-posit16`
3×	`difference-of-squares`
2×	`pow-pow` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `distribute-lft-out--`

Counts

4 → 133

Calls

4 calls:

134.0ms	(* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n)))
20.0ms	(pow (+ x 1) (/ 1 n))
28.0ms	(pow (+ x 1) (/ 1 n))
47.0ms	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) 1)) (pow x (/ 1 n)))

series798.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n)))
144.0ms	(pow (+ x 1) (/ 1 n))
105.0ms	(pow (+ x 1) (/ 1 n))
381.0ms	(- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) 1)) (pow x (/ 1 n)))

simplify2.0s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	1720
1	527
0	192

prune897.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
1.6b	(cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n))))
2.4b	(- (cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow` `*-un-lft-identity`
25×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
9×	`unpow-prod-down`
8×	`associate-*l/`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`cbrt-div` `add-cbrt-cube` `insert-posit16`
3×	`difference-of-squares` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `flip3-+` `frac-add` `pow-exp` `flip-+` `div-inv` `distribute-lft-out`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

11.0ms	(pow (+ x 1) (/ 1 n))
11.0ms	(pow (+ x 1) (/ 1 n))
1.2s	(cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n))))
75.0ms	(- (cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

series3.6s

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (+ x 1) (/ 1 n))
97.0ms	(pow (+ x 1) (/ 1 n))
455.0ms	(cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n))))
2.9s	(- (cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))

simplify2.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	1841
1	573
0	213

prune705.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.3b

regimes465.0ms

Accuracy

83.9% (1.4b remaining)

Error of 22.0b against oracle of 20.6b and baseline of 29.5b

bsearch255.0ms

Steps

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

simplify13.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.9s	3175×	body	1280	valid
958.0ms	626×	body	1280	nan
948.0ms	1569×	body	640	valid
934.0ms	1179×	body	10240	exit
594.0ms	4651×	body	80	valid
436.0ms	5178×	body	80	nan
354.0ms	846×	body	320	valid
338.0ms	631×	body	640	nan
139.0ms	443×	body	160	valid
118.0ms	354×	body	320	nan
31.0ms	166×	body	160	nan