Details

sample318.0ms

Algorithm

intervals

Results

115.0ms	81×	body	1280	valid
107.0ms	34×	body	2560	valid
35.0ms	50×	body	640	valid
14.0ms	107×	body	80	valid
10.0ms	22×	body	320	valid
9.0ms	80×	body	80	nan
8.0ms	1×	body	5120	valid
4.0ms	15×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
5	2006
4	512
3	150
2	58
1	28
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.3b	(- (pow (+ 1 (/ i n)) n) 1)
6.8b	(pow (+ 1 (/ i n)) n)
11.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite518.0ms

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`
4×	`insert-posit16`
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 → 453

Calls

4 calls:

208.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
96.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)
186.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
297.0ms	(- (pow (+ 1 (/ i n)) n) 1)
258.0ms	(pow (+ 1 (/ i n)) n)
399.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.5s

Counts

465 → 465

Iterations

Iter	Nodes
done	2001
2	2001
1	1702
0	542

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.3b	(* 1/6 (* i (* i i)))
5.8b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
18.9b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
83×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
27×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
14×	`distribute-lft-out`
13×	`associate-/r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`flip3-+` `associate-r` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `cube-unmult` `associate-/r/` `pow-sqr` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

13.0ms	(* i (* i i))
32.0ms	(* 1/6 (* i (* i i)))
17.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
156.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

series284.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* i (* i i))
46.0ms	(* 1/6 (* i (* i i)))
128.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))
72.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) (/ i n))

simplify921.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	2001
2	2001
1	648
0	240

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (* i (* i i)))
3.1b	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
4.4b	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
5.8b	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-l`
15×	`pow1`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down` `distribute-lft-out`
6×	`add-log-exp`
4×	`associate-r` `insert-posit16` `associate-/l*`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `*-commutative` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-*l/`

Counts

4 → 104

Calls

4 calls:

46.0ms	(* 1/6 (* i (* i i)))
168.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
193.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
38.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 1/6 (* i (* i i)))
80.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i) n)
49.0ms	(/ (+ (+ (* (* i i) 1/2) (* 1/6 (* i (* i i)))) i) i)
152.0ms	(+ (* (* i i) 1/2) (* 1/6 (* i (* i i))))

simplify1.1s

Counts

116 → 116

Iterations

Iter	Nodes
done	2005
3	2005
2	1636
1	456
0	169

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.3b	(* 1/6 (* i (* i i)))
2.0b	(log (exp (* 1/6 (* i (* i i)))))
5.8b	(+ (* (* i i) 1/2) (log (exp (* 1/6 (* i (* i i))))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`log-prod` `associate-l` `add-log-exp`
5×	`pow-prod-up`
4×	`insert-posit16`
3×	`associate-+r+` `log-pow`
2×	`associate-r` `*-commutative`
1×	`pow2` `+-commutative` `exp-prod` `sum-log` `flip3-+` `pow-plus` `exp-to-pow` `cube-unmult` `rem-log-exp` `pow-sqr` `flip-+` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

13.0ms	(* i (* i i))
33.0ms	(* 1/6 (* i (* i i)))
6.0ms	(log (exp (* 1/6 (* i (* i i)))))
28.0ms	(+ (* (* i i) 1/2) (log (exp (* 1/6 (* i (* i i))))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* i (* i i))
56.0ms	(* 1/6 (* i (* i i)))
64.0ms	(log (exp (* 1/6 (* i (* i i)))))
109.0ms	(+ (* (* i i) 1/2) (log (exp (* 1/6 (* i (* i i))))))

simplify922.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	2003
3	2003
2	743
1	250
0	107

prune712.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.1b

regimes306.0ms

Accuracy

52.1% (10.8b remaining)

Error of 21.9b against oracle of 11.1b and baseline of 33.6b

bsearch448.0ms

Steps

Iters	Range		Point
9	2.732959901816702e-89	4.768362289250455e-83	4.420752440477652e-89
6	-0.13673991589698092	-0.009521407882115243	-0.13295556128930017
6	-5.981261346914101e+64	-9.091852273913624e+63	-1.0933259526011947e+64
7	-1.38761684700311e+113	-8.639618869970432e+110	-1.1051279060415901e+112

simplify17.0ms

Iterations

Iter	Nodes
done	69
1	69
0	50

end0.0ms

sample7.9s

Algorithm

intervals

Results

3.4s	2455×	body	1280	valid
2.4s	998×	body	2560	valid
960.0ms	1537×	body	640	valid
328.0ms	898×	body	320	valid
304.0ms	3055×	body	80	valid
186.0ms	2276×	body	80	nan
118.0ms	456×	body	160	valid
13.0ms	3×	body	5120	valid