Details

sample169.0ms

Algorithm

intervals

Results

73.0ms	38×	body	2560	valid
49.0ms	66×	body	1280	valid
15.0ms	47×	body	640	valid
6.0ms	34×	body	320	valid
5.0ms	100×	body	80	valid
3.0ms	77×	body	80	nan
1.0ms	8×	body	160	valid

simplify4.0s

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: 39.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (- (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:

469.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
253.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms	(pow (+ 1.0 (/ i n)) n)
468.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

465.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
334.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
277.0ms	(pow (+ 1.0 (/ i n)) n)
412.0ms	(/ (- (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

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
72×	`prod-diff`
66×	`add-cube-cbrt`
46×	`unpow-prod-down`
31×	`times-frac`
26×	`distribute-rgt-in` `distribute-lft-in`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r*` `sqr-pow`
11×	`distribute-lft-out`
8×	`fma-neg`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `div-exp` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
2×	`associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

525.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
258.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(pow (+ 1.0 (/ i n)) n)
327.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

305.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
296.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
262.0ms	(pow (+ 1.0 (/ i n)) n)
441.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify2.0s

Counts

210 → 210

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	334	4926
1	774	4025
2	2219	3373
done	5000	3221

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
6.8b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`distribute-rgt-out`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`div-inv`
5×	`add-log-exp`
4×	`pow1` `distribute-lft-neg-out` `unpow-prod-down` `associate-/l*`
3×	`cbrt-undiv` `expm1-log1p-u` `pow-unpow` `div-exp` `log1p-expm1-u`
2×	`flip3-+` `div-sub` `unsub-neg` `flip-+` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `pow-pow` `fma-def` `frac-2neg` `pow-exp` `clear-num` `sum-log` `associate-/r/` `distribute-lft-out` `sqr-pow`

Counts

3 → 127

Calls

3 calls:

42.0ms	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
35.0ms	(pow (+ 1.0 (/ i n)) n)
93.0ms	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

series1.0s

Counts

3 → 9

Calls

3 calls:

303.0ms	(+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0))
267.0ms	(pow (+ 1.0 (/ i n)) n)
449.0ms	(/ (+ (* (pow (+ 1.0 (/ i n)) n) 100.0) (* (- 1.0) 100.0)) (/ i n))

simplify1.6s

Counts

136 → 136

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	279	3504
1	674	2957
2	2315	2804
done	5002	2796

prune483.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.0b	(* n (/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
0.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)

rewrite984.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
72×	`prod-diff`
69×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
46×	`unpow-prod-down`
26×	`distribute-rgt-in` `distribute-lft-in`
16×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`associate-r`
13×	`sqr-pow`
11×	`distribute-lft-out`
9×	`pow1`
8×	`fma-neg`
6×	`associate-l` `add-log-exp` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `times-frac` `associate-*r/`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow-to-exp` `pow-pow` `diff-log` `pow-exp` `div-inv`

Counts

4 → 177

Calls

4 calls:

350.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
276.0ms	(* n (/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
315.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
35.0ms	(pow (+ 1.0 (/ i n)) n)

series919.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
172.0ms	(* n (/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
256.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
226.0ms	(pow (+ 1.0 (/ i n)) n)

simplify1.2s

Counts

189 → 189

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	353	4669
1	835	3779
2	2607	3173
done	5001	3009

prune312.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.4b

regimes159.0ms

Accuracy

45.7% (14.7b remaining)

Error of 21.2b against oracle of 6.5b and baseline of 33.5b

bsearch646.0ms

Steps

Iters	Range		Point
9	3.5235042688903e-96	3.0226105214504583e-87	1.8036192104093916e-92
8	-1.9636081948043714e-305	4.126170549446376e-308	2.6511243075993e-310
8	-8.376792398552119e+65	-6.261927662807804e+61	-2.7257035421547514e+65
8	-2.519337225575135e+155	-4.1822478152609936e+152	-2.480881740905885e+155
7	-1.0921356232246343e+169	-1.1555274265453707e+167	-1.2213511640351215e+167

simplify33.0ms

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	97	278
1	126	270
2	130	270
3	131	270
done	131	270

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.8s	988×	body	2560	valid
1.8s	2507×	body	1280	valid
473.0ms	1564×	body	640	valid
153.0ms	891×	body	320	valid
137.0ms	3043×	body	80	valid
83.0ms	2285×	body	80	nan
46.0ms	433×	body	160	valid
28.0ms	8×	body	5120	valid