Details

sample170.0ms

Algorithm

intervals

Results

62.0ms	82×	body	1280	valid
48.0ms	27×	body	2560	valid
27.0ms	57×	body	640	valid
7.0ms	35×	body	320	valid
6.0ms	106×	body	80	valid
3.0ms	63×	body	80	nan
2.0ms	15×	body	160	valid

simplify33.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.7b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite881.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
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` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

349.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
164.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms	(pow (+ 1.0 (/ i n)) n)
329.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms	(pow (+ 1.0 (/ i n)) n)
366.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify55.0ms

Counts: 293 → 293

prune833.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.1b	(* (pow i 2) (log 1.0))
19.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite587.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

12.0ms	(* 0.5 (pow i 2))
276.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
14.0ms	(* (pow i 2) (log 1.0))
277.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series600.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 0.5 (pow i 2))
222.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
162.0ms	(* (pow i 2) (log 1.0))
189.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify51.0ms

Counts: 212 → 212

prune783.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
15×	`associate-r`
12×	`associate-l`
11×	`prod-exp`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

13.0ms	(* 0.5 (pow i 2))
311.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
276.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms	(* (pow i 2) (log 1.0))

series579.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 0.5 (pow i 2))
230.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
146.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
161.0ms	(* (pow i 2) (log 1.0))

simplify85.0ms

Counts: 124 → 124

prune409.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
0.2b	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite908.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
428×	`add-sqr-sqrt`
399×	`*-un-lft-identity`
397×	`add-cube-cbrt`
178×	`associate-r`
65×	`add-exp-log`
57×	`div-inv`
38×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
12×	`prod-exp`
11×	`associate-l` `unswap-sqr`
7×	`pow1`
6×	`log-prod` `cbrt-unprod`
4×	`unpow-prod-down` `rec-exp` `1-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `associate-*r/` `pow-prod-down` `pow-exp` `log-pow` `flip--`

Counts

4 → 492

Calls

4 calls:

329.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
244.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
286.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms	(* (pow i 2) (log 1.0))

series746.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
200.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
150.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
173.0ms	(* (pow i 2) (log 1.0))

simplify422.0ms

Counts: 504 → 504

prune1.6s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 10.5b

regimes349.0ms

Accuracy

53.4% (10.5b remaining)

Error of 21.8b against oracle of 11.3b and baseline of 33.9b

bsearch539.0ms

Steps

Iters	Range		Point
10	3.025638530234631e-200	3.6681880579996266e-190	1.0105121348641819e-197
7	-5.302367957985033e-272	-1.1484460387677015e-273	-1.4890995792184123e-273
10	-108.06719872485291	-1.177892376223511e-09	-4.6134413143536115
7	-8.794280737794768e+42	-2.2633783743194203e+41	-5.424764060700194e+41
9	-1.6351812353498447e+82	-1.1267852937238848e+76	-4.149010238435241e+81

simplify2.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.5s	1021×	body	2560	valid
2.1s	2400×	body	1280	valid
584.0ms	1650×	body	640	valid
225.0ms	866×	body	320	valid
163.0ms	3079×	body	80	valid
121.0ms	2277×	body	80	nan
57.0ms	459×	body	160	valid
10.0ms	3×	body	5120	valid