Details

sample282.0ms

Algorithm

intervals

Results

106.0ms	76×	body	1280	valid
92.0ms	31×	body	2560	valid
32.0ms	49×	body	640	valid
13.0ms	104×	body	80	valid
12.0ms	24×	body	320	valid
8.0ms	75×	body	80	nan
4.0ms	14×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
6	7318
5	1480
4	419
3	148
2	56
1	26
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.1b	(- (pow (+ 1 (/ i n)) n) 1)
8.0b	(pow (+ 1 (/ i n)) n)
10.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
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 → 449

Calls

4 calls:

191.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
92.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)
218.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

363.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
282.0ms	(- (pow (+ 1 (/ i n)) n) 1)
289.0ms	(pow (+ 1 (/ i n)) n)
376.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify10.8s

Counts

461 → 461

Iterations

Iter	Nodes
2	5426
1	1662
0	538

prune3.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize18.0ms

Local error

Found 3 expressions with local error:

1.1b	(- (pow (+ 1 (/ i n)) n) 1)
8.0b	(pow (+ 1 (/ i n)) n)
10.2b	(/ (* 100 (- (pow (+ 1 (/ i n)) n) 1)) (/ i n))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`associate-/r*`
7×	`unpow-prod-down`
6×	`cbrt-undiv` `div-exp` `difference-of-squares`
5×	`add-log-exp`
4×	`pow1` `sqr-pow`
3×	`pow-unpow` `difference-of-sqr-1` `div-inv`
2×	`flip3--` `prod-exp` `associate-*r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `pow-exp` `associate-/r/` `distribute-lft-out` `associate-/l*` `distribute-lft-out--`

Counts

3 → 88

Calls

3 calls:

91.0ms	(- (pow (+ 1 (/ i n)) n) 1)
12.0ms	(pow (+ 1 (/ i n)) n)
95.0ms	(/ (* 100 (- (pow (+ 1 (/ i n)) n) 1)) (/ i n))

series721.0ms

Counts

3 → 9

Calls

3 calls:

214.0ms	(- (pow (+ 1 (/ i n)) n) 1)
203.0ms	(pow (+ 1 (/ i n)) n)
304.0ms	(/ (* 100 (- (pow (+ 1 (/ i n)) n) 1)) (/ i n))

simplify9.0s

Counts

97 → 97

Iterations

Iter	Nodes
3	10945
2	1952
1	548
0	204

prune539.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.4b	(/ 1 (/ i n))
8.0b	(pow (+ 1 (/ i n)) n)
11.0b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

395×	`times-frac`
286×	`add-sqr-sqrt`
233×	`*-un-lft-identity`
153×	`add-cube-cbrt`
70×	`unpow-prod-down`
35×	`difference-of-squares`
29×	`add-exp-log`
26×	`associate-/r*`
25×	`sqr-pow`
24×	`div-inv`
16×	`div-exp` `distribute-lft-out--`
15×	`distribute-lft-out`
14×	`add-cbrt-cube`
11×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `add-log-exp`
5×	`distribute-rgt-out--` `associate-/r/`
3×	`pow-to-exp` `pow-unpow` `pow-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `pow-pow` `flip3--` `diff-log` `frac-sub` `pow-flip` `flip--` `inv-pow` `sub-div`

Counts

4 → 308

Calls

4 calls:

25.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
5.0ms	(/ 1 (/ i n))
8.0ms	(pow (+ 1 (/ i n)) n)
84.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
9.0ms	(/ 1 (/ i n))
195.0ms	(pow (+ 1 (/ i n)) n)
266.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify2.7s

Counts

320 → 320

Iterations

Iter	Nodes
2	3104
1	1196
0	483

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n)))
0.2b	(* (* (* i i) n) 1/6)
5.4b	(+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n))
9.0b	(* (* i i) n)

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-r` `add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-l`
3×	`sum-log` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in`

Counts

4 → 75

Calls

4 calls:

203.0ms	(* 100 (+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n)))
35.0ms	(* (* (* i i) n) 1/6)
56.0ms	(+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n))
12.0ms	(* (* i i) n)

series104.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 100 (+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n)))
21.0ms	(* (* (* i i) n) 1/6)
30.0ms	(+ (* (* (* i i) n) 1/6) (+ (* (* i 1/2) n) n))
18.0ms	(* (* i i) n)

simplify4.1s

Counts

87 → 87

Iterations

Iter	Nodes
3	9364
2	1648
1	390
0	130

prune450.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.5b

regimes258.0ms

Accuracy

51.2% (11.0b remaining)

Error of 21.9b against oracle of 10.9b and baseline of 33.6b

bsearch458.0ms

Steps

Iters	Range		Point
7	1.4604094432221333e-135	6.06229621642618e-134	9.575664251285104e-135
9	-5.983019040719778e-49	-7.703480879617428e-54	-5.9286511822489366e-49
10	-1.0293047184176334e+23	-6889706126056.061	-9.669625897906558e+22
8	-2.8945583997465117e+50	-1.0151626126287093e+46	-1.7911077630361746e+47
5	-2.948921166850807e+126	-1.3096288762443326e+126	-1.3875157595860486e+126

simplify12.0ms

Iterations

Iter	Nodes
2	60
1	60
0	47

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.4s	1010×	body	2560	valid
2.3s	2391×	body	1280	valid
846.0ms	1666×	body	640	valid
282.0ms	3060×	body	80	valid
262.0ms	866×	body	320	valid
172.0ms	2217×	body	80	nan
110.0ms	446×	body	160	valid
22.0ms	6×	body	5120	valid