Details

sample190.0ms

Algorithm

intervals

Results

80.0ms	76×	body	1280	valid
48.0ms	24×	body	2560	valid
22.0ms	54×	body	640	valid
7.0ms	27×	body	320	valid
6.0ms	98×	body	80	valid
5.0ms	96×	body	80	nan
3.0ms	19×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	140	15
4	347	15
5	1514	15
done	5000	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b	(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`
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:

448.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
187.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
34.0ms	(pow (+ 1.0 (/ i n)) n)
474.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

570.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
356.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
250.0ms	(pow (+ 1.0 (/ i n)) n)
408.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify916.0ms

Counts

293 → 293

Iterations

Useful iterations: done (891.0ms)

Iter	Nodes	Cost
0	437	6469
1	1416	6211
done	5000	5919

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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)))
12.1b	(* (pow i 2) (log 1.0))
16.2b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite841.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

29.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
346.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
25.0ms	(* (pow i 2) (log 1.0))
425.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series781.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
284.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
214.0ms	(* (pow i 2) (log 1.0))
217.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify575.0ms

Counts

198 → 198

Iterations

Useful iterations: done (560.0ms)

Iter	Nodes	Cost
0	338	6829
1	1023	6655
done	5001	6143

prune970.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
3.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
10.3b	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
12.1b	(* (pow i 2) (log 1.0))

rewrite827.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
127×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
53×	`add-exp-log`
48×	`associate-r`
32×	`add-cbrt-cube`
23×	`div-exp`
21×	`associate-l`
13×	`prod-exp` `associate-/r*`
12×	`cbrt-undiv` `unswap-sqr`
10×	`div-inv`
9×	`add-log-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`unpow-prod-down`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 215

Calls

4 calls:

43.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
348.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
386.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
29.0ms	(* (pow i 2) (log 1.0))

series711.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
169.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
286.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
213.0ms	(* (pow i 2) (log 1.0))

simplify615.0ms

Counts

227 → 227

Iterations

Useful iterations: done (605.0ms)

Iter	Nodes	Cost
0	379	8307
1	1243	7916
done	5000	6996

prune891.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.4b

localize33.0ms

Local error

Found 4 expressions with local error:

10.3b	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
12.1b	(* (pow i 2) (log 1.0))
12.1b	(* (pow i 2) (log 1.0))
12.1b	(* (pow i 2) (log 1.0))

rewrite692.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`associate-l`
31×	`add-exp-log`
26×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-cbrt-cube`
18×	`log-prod`
15×	`prod-exp`
13×	`associate-r`
12×	`pow1` `unpow-prod-down` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `cbrt-unprod`
6×	`unpow2` `sqr-pow`
5×	`associate-*l/`
4×	`*-commutative` `add-log-exp`
3×	`pow-to-exp` `pow-prod-down` `pow-exp` `log-pow`
2×	`cbrt-undiv` `frac-times` `flip3--` `associate-*r/` `div-exp` `flip--`
1×	`div-inv`

Counts

4 → 139

Calls

4 calls:

637.0ms	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
17.0ms	(* (pow i 2) (log 1.0))
14.0ms	(* (pow i 2) (log 1.0))
19.0ms	(* (pow i 2) (log 1.0))

series709.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
166.0ms	(* (pow i 2) (log 1.0))
164.0ms	(* (pow i 2) (log 1.0))
163.0ms	(* (pow i 2) (log 1.0))

simplify1.2s

Counts

151 → 151

Iterations

Useful iterations: 2 (333.0ms)

Iter	Nodes	Cost
0	172	2714
1	468	2614
2	2502	2183
done	5002	2183

prune626.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 11.4b

regimes636.0ms

Accuracy

53.4% (10.5b remaining)

Error of 21.4b against oracle of 10.9b and baseline of 33.4b

bsearch509.0ms

Steps

Iters	Range		Point
8	1.7651294170037398e+141	1.8332650139728974e+145	5.064717226083426e+144
10	3.6038887973904155e-15	1575.9184687212278	18.662937204719956
0	3.894337894410089e-198	3.931641926837824e-198	3.912989910623956e-198
6	-1.8476729376770798e-255	-2.387276649835617e-256	-1.4313525468371782e-255
9	-3.309911606533295	-1.716801800522696e-06	-0.10408074195050146

simplify26.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	306
1	80	306
done	80	306

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.3s	2569×	body	1280	valid
2.0s	945×	body	2560	valid
634.0ms	1634×	body	640	valid
425.0ms	2223×	body	80	nan
204.0ms	839×	body	320	valid
203.0ms	2934×	body	80	valid
54.0ms	424×	body	160	valid
18.0ms	5×	body	5120	valid