Details

sample154.0ms

Algorithm

intervals

Results

60.0ms	33×	body	2560	valid
51.0ms	75×	body	1280	valid
15.0ms	53×	body	640	valid
5.0ms	104×	body	80	valid
5.0ms	28×	body	320	valid
2.0ms	69×	body	80	nan
1.0ms	11×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7
done	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b	(pow (+ 1.0 (/ i n)) n)
10.6b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite797.0ms

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:

320.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
152.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(pow (+ 1.0 (/ i n)) n)
291.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

363.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
244.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms	(pow (+ 1.0 (/ i n)) n)
345.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify54.0ms

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166
done	5002	3166

prune764.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 24.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b	(pow (+ 1.0 (/ i n)) n)

rewrite821.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
28×	`associate-r`
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-l` `pow-prod-down` `distribute-lft-out--`
3×	`pow-unpow`
2×	`cbrt-undiv` `associate-r/` `div-exp` `-commutative` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `associate-*l/` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 99

Calls

4 calls:

343.0ms	(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
300.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
156.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(pow (+ 1.0 (/ i n)) n)

series990.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
159.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms	(pow (+ 1.0 (/ i n)) n)

simplify69.0ms

Counts

111 → 111

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	561	927
1	2792	821
2	5001	820
done	5001	820

prune240.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.0b

localize20.0ms

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)
13.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.1b	(* (pow i 2) (log 1.0))

rewrite554.0ms

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:

11.0ms	(* 0.5 (pow i 2))
278.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
248.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))

series513.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
203.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
143.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms	(* (pow i 2) (log 1.0))

simplify78.0ms

Counts

124 → 124

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	525	1450
1	2621	1228
2	5001	1228
done	5001	1228

prune342.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize18.0ms

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)
13.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.1b	(* (pow i 2) (log 1.0))

rewrite559.0ms

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:

11.0ms	(* 0.5 (pow i 2))
279.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
252.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))

series516.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* 0.5 (pow i 2))
206.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
134.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
144.0ms	(* (pow i 2) (log 1.0))

simplify78.0ms

Counts

124 → 124

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	525	1450
1	2621	1228
2	5001	1228
done	5001	1228

prune345.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.0b

regimes142.0ms

Accuracy

48.6% (11.7b remaining)

Error of 22.9b against oracle of 11.1b and baseline of 34.0b

bsearch260.0ms

Steps

Iters	Range	Point
8	1.5934329611832436e-130	4.113531426965663e-127	1.6134148830388508e-130
8	-7.622341151832115e-247	-6.506148429240512e-251	-9.519350012649904e-251
6	-4.3436177944509636e+95	-5.9618745358935405e+94	-7.766937677453618e+94

Iters

Range

Point

1.5934329611832436e-130

4.113531426965663e-127

1.6134148830388508e-130

-7.622341151832115e-247

-6.506148429240512e-251

-9.519350012649904e-251

-4.3436177944509636e+95

-5.9618745358935405e+94

-7.766937677453618e+94

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	50
1	58	50
done	58	50

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.9s	1020×	body	2560	valid
1.7s	2402×	body	1280	valid
463.0ms	1647×	body	640	valid
150.0ms	884×	body	320	valid
129.0ms	3072×	body	80	valid
78.0ms	2291×	body	80	nan
46.0ms	438×	body	160	valid
18.0ms	5×	body	5120	valid