Details

sample285.0ms

Algorithm

intervals

Results

109.0ms	35×	body	2560	valid
87.0ms	76×	body	1280	valid
37.0ms	53×	body	640	valid
8.0ms	25×	body	320	valid
8.0ms	96×	body	80	valid
6.0ms	90×	body	80	nan
3.0ms	15×	body	160	valid

simplify1.3s

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	1535	15
done	5000	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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` `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 → 281

Calls

4 calls:

437.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
207.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
394.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

463.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
378.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
363.0ms	(pow (+ 1.0 (/ i n)) n)
459.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify688.0ms

Counts

293 → 293

Iterations

Useful iterations: done (673.0ms)

Iter	Nodes	Cost
0	437	6469
1	1418	6209
done	5001	5917

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (* 0.5 (pow i 2)))
0.1b	(* 100.0 (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
10.4b	(* (log 1.0) (pow i 2))
17.2b	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (* 0.5 (pow i 2)))
197.0ms	(* 100.0 (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
11.0ms	(* (log 1.0) (pow i 2))
194.0ms	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

series622.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (* 1.0 i) (* 0.5 (pow i 2)))
203.0ms	(* 100.0 (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
155.0ms	(* (log 1.0) (pow i 2))
192.0ms	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

simplify364.0ms

Counts

190 → 190

Iterations

Useful iterations: done (352.0ms)

Iter	Nodes	Cost
0	326	6616
1	1035	6470
done	5001	5985

prune971.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (* 0.5 (pow i 2)))
2.5b	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
10.4b	(* (log 1.0) (pow i 2))
13.0b	(* (/ 100.0 i) (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

rewrite437.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 207

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (* 0.5 (pow i 2)))
193.0ms	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
10.0ms	(* (log 1.0) (pow i 2))
219.0ms	(* (/ 100.0 i) (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

series588.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (* 1.0 i) (* 0.5 (pow i 2)))
149.0ms	(/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
148.0ms	(* (log 1.0) (pow i 2))
215.0ms	(* (/ 100.0 i) (/ (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

simplify422.0ms

Counts

219 → 219

Iterations

Useful iterations: done (413.0ms)

Iter	Nodes	Cost
0	366	8094
1	1259	7714
done	5001	6817

prune943.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize37.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
4.8b	(/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i))
7.5b	(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i)))
10.4b	(* (log 1.0) (pow i 2))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

74×	`add-exp-log`
51×	`add-cbrt-cube`
33×	`add-sqr-sqrt`
32×	`prod-exp`
30×	`cbrt-unprod`
21×	`associate-r`
20×	`cbrt-undiv` `times-frac` `div-exp`
19×	`*-un-lft-identity` `add-cube-cbrt`
17×	`associate-l`
9×	`cbrt-prod` `pow1`
8×	`unswap-sqr`
6×	`associate-/r*`
5×	`associate-*l/`
4×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
3×	`associate-r/` `-commutative` `div-inv`
2×	`flip3--` `pow-prod-down` `flip--` `unpow2` `sqr-pow` `associate-/l/`
1×	`frac-times` `pow-to-exp` `clear-num` `frac-2neg` `pow-exp` `log-pow` `associate-/l*`

Counts

4 → 138

Calls

4 calls:

285.0ms	(* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
359.0ms	(/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i))
424.0ms	(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i)))
10.0ms	(* (log 1.0) (pow i 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
651.0ms	(/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i))
452.0ms	(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (/ (* (sqrt 100.0) (* (- (+ (* (log 1.0) n) (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)) (cbrt i)))
155.0ms	(* (log 1.0) (pow i 2))

simplify311.0ms

Counts

150 → 150

Iterations

Useful iterations: done (305.0ms)

Iter	Nodes	Cost
0	309	5986
1	969	5740
done	5000	4423

prune703.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.4b

regimes333.0ms

Accuracy

43.2% (12.6b remaining)

Error of 23.5b against oracle of 11.0b and baseline of 33.1b

bsearch470.0ms

Steps

Iters	Range		Point
7	1.2245728681896357e-155	1.2152850197652755e-153	1.4183297845116364e-154
7	-22.8286883066892	-0.10952899301968014	-1.8594290872480363
8	-8.389936357340607e+106	-5.720382841890011e+103	-8.23875326441092e+106
7	-4.1468841507459867e+123	-2.615624459402513e+121	-6.142887410522618e+122

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	48	150
1	69	122
done	69	122

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	2450×	body	1280	valid
1.9s	995×	body	2560	valid
543.0ms	1640×	body	640	valid
346.0ms	2189×	body	80	nan
202.0ms	3041×	body	80	valid
180.0ms	835×	body	320	valid
78.0ms	454×	body	160	valid
25.0ms	7×	body	5120	valid