Details

sample294.0ms

Algorithm

intervals

Results

111.0ms	41×	body	2560	valid
92.0ms	77×	body	1280	valid
32.0ms	28×	body	320	valid
23.0ms	37×	body	640	valid
10.0ms	85×	body	80	valid
9.0ms	77×	body	80	nan
5.0ms	19×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.6b	(- (pow (+ 1 (/ i n)) n) 1)
9.2b	(pow (+ 1 (/ i n)) n)
12.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite592.0ms

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:

236.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
105.0ms	(- (pow (+ 1 (/ i n)) n) 1)
16.0ms	(pow (+ 1 (/ i n)) n)
221.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

393.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
284.0ms	(- (pow (+ 1 (/ i n)) n) 1)
247.0ms	(pow (+ 1 (/ i n)) n)
361.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify9.0s

Counts

465 → 465

Iterations

Iter	Nodes
2	5274
1	1671
0	542

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 1/6 (* i i)) i)
0.2b	(* 1/6 (* i i))
9.5b	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
20.8b	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

40.0ms	(* (* 1/6 (* i i)) i)
15.0ms	(* 1/6 (* i i))
17.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
173.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

series247.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 1/6 (* i i)) i)
31.0ms	(* 1/6 (* i i))
104.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
71.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

simplify1.0s

Counts

153 → 153

Iterations

Iter	Nodes
2	2493
1	657
0	237

prune915.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 16.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (* i i))
3.3b	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
4.0b	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
9.5b	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

rewrite381.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

14.0ms	(* 1/6 (* i i))
165.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
183.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
17.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

series251.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 (* i i))
52.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
71.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
101.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

simplify3.4s

Counts

114 → 114

Iterations

Iter	Nodes
3	7720
2	1572
1	450
0	163

prune630.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* i (* i (+ (* 1/6 i) 1/2)))
0.1b	(* i (+ (* 1/6 i) 1/2))
0.3b	(* 1/6 i)
1.1b	(log (exp (* i (* i (+ (* 1/6 i) 1/2)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `pow1`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
7×	`log-prod` `associate-r`
6×	`associate-*r/`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`exp-sum` `insert-posit16`
3×	`log-pow` `*-commutative`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

31.0ms	(* i (* i (+ (* 1/6 i) 1/2)))
20.0ms	(* i (+ (* 1/6 i) 1/2))
6.0ms	(* 1/6 i)
6.0ms	(log (exp (* i (* i (+ (* 1/6 i) 1/2)))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* i (* i (+ (* 1/6 i) 1/2)))
65.0ms	(* i (+ (* 1/6 i) 1/2))
15.0ms	(* 1/6 i)
70.0ms	(log (exp (* i (* i (+ (* 1/6 i) 1/2)))))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
3	3931
2	896
1	297
0	135

prune561.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.2b

regimes386.0ms

Accuracy

50.9% (11.0b remaining)

Error of 21.9b against oracle of 10.9b and baseline of 33.4b

bsearch475.0ms

Steps

Iters	Range		Point
10	4.422991971728374e-183	1.6714674345894424e-164	3.760450716247655e-168
11	-774963815.1405225	-6.948120050383171e-19	-1.4249003372371525
8	-9.96884557711962e+51	-1.8352256695695305e+49	-3.866080760544941e+49
6	-2.4718491359766566e+134	-2.579862417768351e+133	-3.094835530129789e+133

simplify12.0ms

Iterations

Iter	Nodes
2	54
1	54
0	40

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	990×	body	2560	valid
2.4s	2499×	body	1280	valid
747.0ms	1595×	body	640	valid
432.0ms	2323×	body	80	nan
286.0ms	3022×	body	80	valid
285.0ms	825×	body	320	valid
93.0ms	425×	body	160	valid
24.0ms	7×	body	5120	valid