Details

sample243.0ms

Algorithm

intervals

Results

93.0ms	37×	body	2560	valid
84.0ms	77×	body	1280	valid
25.0ms	46×	body	640	valid
10.0ms	93×	body	80	valid
10.0ms	25×	body	320	valid
6.0ms	60×	body	80	nan
4.0ms	14×	body	160	valid

simplify4.1s

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: 40.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.1b	(- (pow (+ 1 (/ i n)) n) 1)
6.2b	(pow (+ 1 (/ i n)) n)
11.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite482.0ms

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:

176.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
115.0ms	(- (pow (+ 1 (/ i n)) n) 1)
10.0ms	(pow (+ 1 (/ i n)) n)
164.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

367.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
266.0ms	(- (pow (+ 1 (/ i n)) n) 1)
289.0ms	(pow (+ 1 (/ i n)) n)
342.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify9.2s

Counts

465 → 465

Iterations

Iter	Nodes
2	5274
1	1671
0	542

prune3.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.3b	(/ 1 (/ i n))
6.2b	(pow (+ 1 (/ i n)) n)
13.9b	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite151.0ms

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/`
4×	`insert-posit16`
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 → 312

Calls

4 calls:

30.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
6.0ms	(/ 1 (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)
99.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series786.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (pow (+ 1 (/ i n)) n) (/ i n))
9.0ms	(/ 1 (/ i n))
218.0ms	(pow (+ 1 (/ i n)) n)
291.0ms	(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify2.5s

Counts

324 → 324

Iterations

Iter	Nodes
2	3035
1	1199
0	487

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6)))))
0.2b	(* (* i i) 1/6)
4.0b	(+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6))))
7.2b	(* n (* (* i i) 1/6))

rewrite130.0ms

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×	`add-log-exp`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `associate-+r+` `distribute-lft-in`

Counts

4 → 79

Calls

4 calls:

59.0ms	(* 100 (+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6)))))
14.0ms	(* (* i i) 1/6)
22.0ms	(+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6))))
34.0ms	(* n (* (* i i) 1/6))

series122.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* 100 (+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6)))))
26.0ms	(* (* i i) 1/6)
34.0ms	(+ (* (* 1/2 i) n) (+ n (* n (* (* i i) 1/6))))
29.0ms	(* n (* (* i i) 1/6))

simplify2.9s

Counts

91 → 91

Iterations

Iter	Nodes
3	9084
2	1663
1	383
0	135

prune559.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 50 i) n)
0.3b	(* (* i i) 50/3)
2.9b	(* (+ 100 (* (* i i) 50/3)) n)
4.0b	(+ (* (* 50 i) n) (* (+ 100 (* (* i i) 50/3)) n))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

15.0ms	(* (* 50 i) n)
14.0ms	(* (* i i) 50/3)
11.0ms	(* (+ 100 (* (* i i) 50/3)) n)
15.0ms	(+ (* (* 50 i) n) (* (+ 100 (* (* i i) 50/3)) n))

series127.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 50 i) n)
26.0ms	(* (* i i) 50/3)
46.0ms	(* (+ 100 (* (* i i) 50/3)) n)
35.0ms	(+ (* (* 50 i) n) (* (+ 100 (* (* i i) 50/3)) n))

simplify3.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	5349
2	1355
1	373
0	130

prune457.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.2b

regimes200.0ms

Accuracy

55.9% (11.9b remaining)

Error of 18.1b against oracle of 6.2b and baseline of 33.3b

bsearch212.0ms

Steps

Iters	Range		Point
10	9.569100293735598e-08	43862.50504651285	1.4921312295942013
5	-737653.907965734	-246175.07200187352	-249306.0470798354

simplify6.0ms

Iterations

Iter	Nodes
2	45
1	45
0	35

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.6s	2514×	body	1280	valid
2.1s	994×	body	2560	valid
862.0ms	1614×	body	640	valid
340.0ms	3079×	body	80	valid
290.0ms	836×	body	320	valid
162.0ms	2265×	body	80	nan
76.0ms	416×	body	160	valid
32.0ms	9×	body	5120	valid