Details

sample241.0ms

Algorithm

intervals

Results

95.0ms	84×	body	1280	valid
73.0ms	24×	body	2560	valid
26.0ms	59×	body	640	valid
8.0ms	24×	body	320	valid
7.0ms	99×	body	80	valid
4.0ms	1×	body	5120	valid
4.0ms	68×	body	80	nan
2.0ms	8×	body	160	valid

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	414
1	25	414
2	59	414
3	135	414
4	309	414
5	836	414
6	3302	414
done	5015	414

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (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:

462.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
183.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
371.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

537.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
368.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
276.0ms	(pow (+ 1.0 (/ i n)) n)
447.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify4.0s

Counts

293 → 293

Iterations

Useful iterations: 2 (2.4s)

Iter	Nodes	Cost
0	437	186805
1	1390	179104
2	4676	175769
done	5001	175769

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
0.1b	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
1.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)

rewrite658.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`associate-l`
22×	`times-frac`
19×	`add-exp-log` `add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`pow1` `difference-of-squares`
8×	`unpow-prod-down`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sqr-pow`
4×	`associate-r` `pow-prod-down` `distribute-lft-out--`
3×	`pow-unpow`
2×	`cbrt-undiv` `div-exp` `associate-l/` `-commutative` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `associate-*r/` `div-inv` `flip--` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

287.0ms	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
214.0ms	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
135.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
373.0ms	(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
220.0ms	(pow (+ 1.0 (/ i n)) n)

simplify1.8s

Counts

111 → 111

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	210	54944
1	567	51819
2	1549	49858
done	5000	49178

prune392.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (- (* i i) (* (log 1.0) (* i i))))
0.1b	(* 100.0 (* (/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i) n))
11.5b	(/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i)
12.1b	(* (log 1.0) (* i i))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
17×	`pow1`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l`
9×	`times-frac` `prod-exp` `cbrt-unprod`
7×	`pow-prod-down` `associate-*r/`
6×	`associate-/l/`
5×	`associate-r`
4×	`frac-add` `add-log-exp`
3×	`associate-/r` `flip3-+` `flip3--` `-commutative` `flip-+` `flip--` `associate-/l*`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-*l/` `log-pow` `div-inv`

Counts

4 → 98

Calls

4 calls:

20.0ms	(* 0.5 (- (* i i) (* (log 1.0) (* i i))))
55.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i) n))
66.0ms	(/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i)
13.0ms	(* (log 1.0) (* i i))

series686.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* 0.5 (- (* i i) (* (log 1.0) (* i i))))
193.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i) n))
141.0ms	(/ (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) i)
144.0ms	(* (log 1.0) (* i i))

simplify2.1s

Counts

110 → 110

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	211	49443
1	633	46619
2	2428	45939
done	5000	45856

prune448.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n))
1.7b	(* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)
12.1b	(* (log 1.0) (* i i))
12.7b	(/ (* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)) i)

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-*r/`
18×	`associate-*l/`
17×	`pow1`
13×	`add-sqr-sqrt`
12×	`frac-add`
10×	`-un-lft-identity` `associate-l*` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`flip3-+` `flip-+`
7×	`pow-prod-down`
6×	`flip3--` `flip--` `associate-/l/`
5×	`associate-r`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/r` `times-frac` `div-exp` `-commutative`
2×	`unswap-sqr`
1×	`clear-num` `frac-2neg` `log-pow` `div-inv` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

82.0ms	(* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n))
74.0ms	(* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)
13.0ms	(* (log 1.0) (* i i))
83.0ms	(/ (* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)) i)

series637.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n))
142.0ms	(* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)
149.0ms	(* (log 1.0) (* i i))
193.0ms	(/ (* 100.0 (* (+ (+ (* (log 1.0) n) (* 1.0 i)) (* 0.5 (- (* i i) (* (log 1.0) (* i i))))) n)) i)

simplify2.4s

Counts

109 → 109

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	219	61126
1	749	54083
2	3628	53643
done	5006	53643

prune425.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.0b

regimes328.0ms

Accuracy

51.8% (11.1b remaining)

Error of 22.0b against oracle of 10.8b and baseline of 33.9b

bsearch939.0ms

Steps

Iters	Range		Point
9	172837025096415.12	4.3123677039784593e+21	176217786659469.75
10	1.610089599574912e-70	9.107827051966749e-58	1.6668266874068228e-69
7	-3.795188455732613e-105	-5.995636585357086e-107	-1.0712482862995937e-106
10	-8.386890221429651e-30	-4.4607380950102347e-41	-8.271685620893128e-30

simplify40.0ms

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	62	2890
1	86	2890
done	86	2890

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.2s	2480×	body	1280	valid
1.9s	996×	body	2560	valid
595.0ms	1604×	body	640	valid
209.0ms	814×	body	320	valid
208.0ms	3164×	body	80	valid
145.0ms	2189×	body	80	nan
46.0ms	401×	body	160	valid
34.0ms	10×	body	5120	valid