Details

sample219.0ms

Algorithm

intervals

Results

77.0ms	70×	body	1280	valid
73.0ms	30×	body	2560	valid
28.0ms	60×	body	640	valid
8.0ms	103×	body	80	valid
6.0ms	25×	body	320	valid
4.0ms	71×	body	80	nan
2.0ms	15×	body	160	valid

simplify669.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (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` `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:

362.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
218.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms	(pow (+ 1.0 (/ i n)) n)
500.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

555.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
372.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
321.0ms	(pow (+ 1.0 (/ i n)) n)
492.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify704.0ms

Counts: 293 → 293

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.6b

localize38.0ms

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)))
11.9b	(* (pow i 2) (log 1.0))
19.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite1.1s

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:

17.0ms	(* 0.5 (pow i 2))
421.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
22.0ms	(* (pow i 2) (log 1.0))
593.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series709.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 0.5 (pow i 2))
264.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
191.0ms	(* (pow i 2) (log 1.0))
220.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify491.0ms

Counts: 212 → 212

prune787.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
11.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.9b	(* (pow i 2) (log 1.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

364.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
310.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
392.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
32.0ms	(* (pow i 2) (log 1.0))

series911.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
269.0ms	(* 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	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
192.0ms	(* (pow i 2) (log 1.0))

simplify1.1s

Counts: 129 → 129

prune535.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 10.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
3.1b	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
11.3b	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
11.9b	(* (pow i 2) (log 1.0))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

716.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
520.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
710.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
32.0ms	(* (pow i 2) (log 1.0))

series885.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
166.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
273.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
241.0ms	(* (pow i 2) (log 1.0))

simplify1.3s

Counts: 111 → 111

prune382.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 10.3b

regimes450.0ms

Accuracy

51.7% (11.1b remaining)

Error of 21.8b against oracle of 10.7b and baseline of 33.6b

bsearch538.0ms

Steps

Iters	Range		Point
7	5.97022637075214e-182	4.447196109763325e-180	3.826192419795082e-180
10	-3.200659746757499e-268	-5.019096545461812e-278	-8.008038266577732e-273
9	-38846.215276402996	-0.2633679361732773	-2.0295365707946575
9	-4.9893541583345076e+36	-7.11546531958759e+28	-9.231162088054738e+32
8	-5.748060931834206e+49	-9.739680168891101e+45	-7.830395539294896e+46

simplify1.3s

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.2s	2453×	body	1280	valid
1.9s	921×	body	2560	valid
539.0ms	1593×	body	640	valid
390.0ms	2258×	body	80	nan
215.0ms	3201×	body	80	valid
185.0ms	805×	body	320	valid
60.0ms	477×	body	160	valid
16.0ms	4×	body	5120	valid