Details

sample253.0ms

Algorithm

intervals

Results

87.0ms	80×	body	1280	valid
83.0ms	34×	body	2560	valid
23.0ms	40×	body	640	valid
23.0ms	57×	body	80	nan
9.0ms	28×	body	320	valid
9.0ms	88×	body	80	valid
4.0ms	19×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4317
4	623
3	163
2	66
1	28
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.7b	(- (pow (+ 1 (/ i n)) n) 1)
6.1b	(pow (+ 1 (/ i n)) n)
11.4b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `distribute-lft-out`

Counts

4 → 453

Calls

4 calls:

209.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
92.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
174.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

385.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
288.0ms	(- (pow (+ 1 (/ i n)) n) 1)
246.0ms	(pow (+ 1 (/ i n)) n)
394.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.1s

Counts

465 → 465

Iterations

Iter	Nodes
done	5000
1	1807
0	542

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.7b	(log (exp (- (pow (+ 1 (/ i n)) n) 1)))
1.7b	(- (pow (+ 1 (/ i n)) n) 1)
6.1b	(pow (+ 1 (/ i n)) n)
11.4b	(/ (log (exp (- (pow (+ 1 (/ i n)) n) 1))) (/ i n))

rewrite882.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
306×	`add-sqr-sqrt`
244×	`*-un-lft-identity`
210×	`log-pow`
195×	`exp-prod`
162×	`add-cube-cbrt`
96×	`difference-of-squares`
52×	`unpow-prod-down`
49×	`sqr-pow`
48×	`difference-of-sqr-1`
20×	`pow1`
19×	`div-inv`
17×	`associate-/l*`
16×	`distribute-lft-out--`
13×	`associate-/r*`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`add-log-exp`
5×	`log-prod`
4×	`insert-posit16`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`log-div` `sub-neg` `exp-diff` `exp-sum`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `flip3--` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `associate-/r/` `flip--` `distribute-lft-out`

Counts

4 → 339

Calls

4 calls:

175.0ms	(log (exp (- (pow (+ 1 (/ i n)) n) 1)))
96.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
588.0ms	(/ (log (exp (- (pow (+ 1 (/ i n)) n) 1))) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

290.0ms	(log (exp (- (pow (+ 1 (/ i n)) n) 1)))
302.0ms	(- (pow (+ 1 (/ i n)) n) 1)
301.0ms	(pow (+ 1 (/ i n)) n)
393.0ms	(/ (log (exp (- (pow (+ 1 (/ i n)) n) 1))) (/ i n))

simplify1.3s

Counts

351 → 351

Iterations

Iter	Nodes
done	5001
1	1474
0	504

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.1b

localize59.0ms

Local error

Found 4 expressions with local error:

6.1b	(pow (+ 1 (/ i n)) n)
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
29×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`unpow-prod-down` `add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `pow1/3` `div-inv`
1×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

14.0ms	(pow (+ 1 (/ i n)) n)
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))

series551.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(pow (+ 1 (/ i n)) n)
88.0ms	(cbrt (/ i n))
67.0ms	(cbrt (/ i n))
96.0ms	(cbrt (/ i n))

simplify969.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	1662
2	507
1	212
0	112

prune776.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.1b

localize84.0ms

Local error

Found 4 expressions with local error:

17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))
17.2b	(cbrt (/ i n))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
36×	`times-frac`
32×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `cbrt-div` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `div-inv` `add-log-exp`

Counts

4 → 92

Calls

4 calls:

2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))
2.0ms	(cbrt (/ i n))

series310.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(cbrt (/ i n))
78.0ms	(cbrt (/ i n))
77.0ms	(cbrt (/ i n))
86.0ms	(cbrt (/ i n))

simplify2.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
4	3000
3	632
2	211
1	113
0	77

prune670.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.1b

regimes210.0ms

Accuracy

53.3% (10.1b remaining)

Error of 31.4b against oracle of 21.4b and baseline of 42.9b

bsearch301.0ms

Steps

Iters	Range		Point
5	4.393655805300957e-149	1.113915902696133e-148	9.072873111493527e-149
8	-1763.0658270955876	-0.28008678268591264	-1.901514792923964
4	-1.5125315820373007e+85	-8.927875500473959e+84	-1.260760569041402e+85

simplify14.0ms

Iterations

Iter	Nodes
done	46
1	46
0	33

end0.0ms

sample9.0s

Algorithm

intervals

Results

3.7s	2486×	body	1280	valid
2.7s	993×	body	2560	valid
1.1s	1615×	body	640	valid
419.0ms	3065×	body	80	valid
373.0ms	842×	body	320	valid
320.0ms	2210×	body	80	nan
113.0ms	449×	body	160	valid
28.0ms	7×	body	5120	valid