Details

sample306.0ms

Algorithm

intervals

Results

114.0ms	77×	body	1280	valid
77.0ms	25×	body	2560	valid
46.0ms	56×	body	640	valid
20.0ms	8×	body	160	valid
14.0ms	110×	body	80	valid
11.0ms	25×	body	320	valid
8.0ms	72×	body	80	nan

simplify4.8s

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: 41.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
7.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
8.0b	(pow (+ 1 (/ i n)) n)

rewrite504.0ms

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:

178.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
113.0ms	(- (pow (+ 1 (/ i n)) n) 1)
182.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
9.0ms	(pow (+ 1 (/ i n)) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
278.0ms	(- (pow (+ 1 (/ i n)) n) 1)
402.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
301.0ms	(pow (+ 1 (/ i n)) n)

simplify5.8s

Counts

465 → 465

Iterations

Iter	Nodes
2	4987
1	1669
0	542

prune3.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n))
0.0b	(* 100 (/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
8.0b	(pow (+ 1 (/ i n)) n)

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

2967×	`times-frac`
1839×	`add-sqr-sqrt`
1490×	`*-un-lft-identity`
1076×	`add-cube-cbrt`
564×	`associate-r`
492×	`difference-of-squares`
250×	`unpow-prod-down`
247×	`sqr-pow`
246×	`difference-of-sqr-1`
116×	`div-inv`
82×	`distribute-lft-out--`
59×	`add-exp-log`
43×	`associate-/l*`
34×	`add-cbrt-cube`
32×	`div-exp`
16×	`cbrt-undiv`
13×	`associate-/r*`
9×	`prod-exp`
7×	`pow1` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `insert-posit16`
3×	`pow-unpow` `associate-l`
2×	`div-sub` `associate-/r/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `flip--` `distribute-lft-out` `associate-/l/`

Counts

4 → 1282

Calls

4 calls:

145.0ms	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n))
223.0ms	(* 100 (/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n)))
81.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

329.0ms	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n))
356.0ms	(* 100 (/ (/ (- (pow (+ 1 (/ i n)) n) 1) i) (/ 1 n)))
267.0ms	(- (pow (+ 1 (/ i n)) n) 1)
273.0ms	(pow (+ 1 (/ i n)) n)

simplify22.5s

Counts

1294 → 1294

Iterations

Iter	Nodes
1	4507
0	1374

prune10.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* i (* i i)))
3.2b	(/ (/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i) (/ 1 n))
3.5b	(/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i)
8.3b	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

430×	`times-frac`
209×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
37×	`add-exp-log`
30×	`div-inv`
27×	`add-cbrt-cube`
17×	`div-exp`
16×	`associate-/r` `associate-/l`
13×	`pow1`
9×	`cbrt-undiv` `add-log-exp`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`sum-log` `associate-l` `associate-/l/`
2×	`rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-r` `associate-/r/` `*-commutative`

Counts

4 → 286

Calls

4 calls:

30.0ms	(* 1/6 (* i (* i i)))
57.0ms	(/ (/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i) (/ 1 n))
60.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i)
29.0ms	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))

series186.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 1/6 (* i (* i i)))
65.0ms	(/ (/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i) (/ 1 n))
51.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))) i)
28.0ms	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))

simplify2.7s

Counts

298 → 298

Iterations

Iter	Nodes
2	3673
1	1484
0	492

prune2.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.7b

localize57.0ms

Local error

Found 4 expressions with local error:

8.3b	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))
18.6b	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
18.6b	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
18.6b	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`sum-log` `pow1/3`
1×	`+-commutative` `associate-+l+`

Counts

4 → 56

Calls

4 calls:

25.0ms	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))
15.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
14.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
14.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i))))
58.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
61.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))
61.0ms	(cbrt (+ (+ i (* (* i i) 1/2)) (* 1/6 (* i (* i i)))))

simplify1.3s

Counts

68 → 68

Iterations

Iter	Nodes
3	3653
2	792
1	236
0	95

prune688.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

regimes150.0ms

Accuracy

52.8% (10.6b remaining)

Error of 21.6b against oracle of 11.1b and baseline of 33.5b

bsearch214.0ms

Steps

Iters	Range	Point
6	1.7721871376884182e-107	9.734453738284303e-107	2.3277881727215845e-107
8	-3.216242211523733e-85	-1.272193222639997e-88	-3.1597532325517974e-85
6	-5.633884575920602e+69	-7.509244231939787e+68	-4.152610626697651e+69

Iters

Range

Point

1.7721871376884182e-107

9.734453738284303e-107

2.3277881727215845e-107

-3.216242211523733e-85

-1.272193222639997e-88

-3.1597532325517974e-85

-5.633884575920602e+69

-7.509244231939787e+68

-4.152610626697651e+69

simplify8.0ms

Iterations

Iter	Nodes
2	53
1	53
0	39

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.3s	2517×	body	1280	valid
2.1s	993×	body	2560	valid
766.0ms	1604×	body	640	valid
580.0ms	871×	body	320	valid
446.0ms	2295×	body	80	nan
328.0ms	2993×	body	80	valid
94.0ms	416×	body	160	valid
54.0ms	13×	body	5120	valid