Details

sample253.0ms

Algorithm

intervals

Results

97.0ms	82×	body	1280	valid
81.0ms	28×	body	2560	valid
26.0ms	49×	body	640	valid
8.0ms	26×	body	320	valid
8.0ms	97×	body	80	valid
6.0ms	91×	body	80	nan
3.0ms	13×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	60	15
3	143	15
4	355	15
5	1077	15
6	4429	15
done	5000	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
9.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative`

Counts

4 → 321

Calls

4 calls:

505.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
230.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms	(pow (+ 1.0 (/ i n)) n)
383.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

482.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
350.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
306.0ms	(pow (+ 1.0 (/ i n)) n)
497.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.4s

Counts

333 → 333

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	479	7415
1	1275	6800
2	3940	6406
done	5000	6350

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ n (/ i (- (pow (/ i n) n) 1.0)))
0.1b	(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
1.1b	(- (pow (/ i n) n) 1.0)
4.6b	(pow (/ i n) n)

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

418×	`times-frac`
393×	`add-sqr-sqrt`
252×	`*-un-lft-identity`
208×	`add-cube-cbrt`
109×	`unpow-prod-down`
95×	`associate-r`
88×	`difference-of-squares`
51×	`prod-diff`
30×	`associate-/r*`
27×	`sqr-pow`
22×	`distribute-lft-out--`
21×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`fma-neg`
16×	`associate-/r/`
14×	`div-inv`
8×	`flip3--` `flip--`
7×	`pow1` `div-exp`
6×	`cbrt-undiv` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`pow-exp`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 376

Calls

4 calls:

82.0ms	(/ n (/ i (- (pow (/ i n) n) 1.0)))
184.0ms	(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
73.0ms	(- (pow (/ i n) n) 1.0)
10.0ms	(pow (/ i n) n)

series476.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ n (/ i (- (pow (/ i n) n) 1.0)))
178.0ms	(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
98.0ms	(- (pow (/ i n) n) 1.0)
55.0ms	(pow (/ i n) n)

simplify1.5s

Counts

388 → 388

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	657	8161
1	1598	7226
done	5001	6788

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
0.1b	(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
1.1b	(- (pow (/ i n) n) 1.0)
4.6b	(pow (/ i n) n)

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

415×	`times-frac`
383×	`add-sqr-sqrt`
251×	`*-un-lft-identity`
207×	`add-cube-cbrt`
109×	`unpow-prod-down`
95×	`associate-r`
88×	`difference-of-squares`
63×	`add-exp-log`
51×	`prod-diff`
30×	`associate-/r*` `add-cbrt-cube`
27×	`sqr-pow`
22×	`div-exp` `distribute-lft-out--`
21×	`prod-exp`
17×	`fma-neg`
16×	`associate-/r/`
14×	`div-inv`
11×	`pow1`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`flip3--` `flip--`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `pow-prod-down` `associate-/l*`
2×	`pow-exp`
1×	`pow-to-exp` `sub-neg` `pow-flip` `pow-pow` `frac-2neg` `diff-log` `associate-r/` `associate-l` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 393

Calls

4 calls:

55.0ms	(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
113.0ms	(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
73.0ms	(- (pow (/ i n) n) 1.0)
10.0ms	(pow (/ i n) n)

series441.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
162.0ms	(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
87.0ms	(- (pow (/ i n) n) 1.0)
73.0ms	(pow (/ i n) n)

simplify2.9s

Counts

405 → 405

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	661	8676
1	1769	7090
2	4840	6381
done	5000	6376

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
6.1b	(pow (+ 1.0 (/ i n)) n)
6.1b	(pow (+ 1.0 (/ i n)) n)

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
29×	`unpow-prod-down`
26×	`add-cube-cbrt`
24×	`prod-diff`
9×	`pow-unpow`
8×	`fma-neg` `sqr-pow`
7×	`pow1` `add-exp-log` `distribute-lft-out`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 110

Calls

4 calls:

205.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms	(pow (+ 1.0 (/ i n)) n)
18.0ms	(pow (+ 1.0 (/ i n)) n)
24.0ms	(pow (+ 1.0 (/ i n)) n)

series995.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
236.0ms	(pow (+ 1.0 (/ i n)) n)
242.0ms	(pow (+ 1.0 (/ i n)) n)
237.0ms	(pow (+ 1.0 (/ i n)) n)

simplify1.5s

Counts

122 → 122

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	129	1939
1	278	1579
2	576	1414
3	1794	1282
done	5001	1252

prune330.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 16.7b

regimes191.0ms

Accuracy

51.7% (13.2b remaining)

Error of 30.0b against oracle of 16.8b and baseline of 44.1b

bsearch563.0ms

Steps

Iters	Range		Point
7	1.466106254315184e+230	4.2050101804867395e+231	2.568245662391043e+231
11	3.173232095275158e+114	4.61796087672408e+142	9.944860624286458e+141
9	1.2167838917470026e-32	3.39002248453449e-27	3.332988420430884e-27
9	-123126161593.44334	-41918.349557210015	-42606.74875587942

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	91	217
1	117	217
done	117	217

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	989×	body	2560	valid
1.9s	2515×	body	1280	valid
521.0ms	1615×	body	640	valid
256.0ms	856×	body	320	valid
209.0ms	2973×	body	80	valid
159.0ms	2337×	body	80	nan
83.0ms	443×	body	160	valid
15.0ms	4×	body	5120	valid