Details

sample103.0ms

Algorithm

intervals

Results

28.0ms	58×	body	1280	valid
25.0ms	291×	body	80	nan
12.0ms	42×	body	640	valid
10.0ms	128×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (log (+ 1.0 N)) (log N))
3.2b	(log (+ 1.0 N))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

10.0ms	(- (log (+ 1.0 N)) (log N))
6.0ms	(log (+ 1.0 N))

series199.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(- (log (+ 1.0 N)) (log N))
65.0ms	(log (+ 1.0 N))

simplify1.4s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	2683
2	637
1	213
0	100

prune281.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.3b	(log (/ (+ N 1.0) N))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

17.0ms	(/ (+ N 1.0) N)
5.0ms	(log (/ (+ N 1.0) N))

series180.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (+ N 1.0) N)
121.0ms	(log (/ (+ N 1.0) N))

simplify878.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1007
1	243
0	108

prune292.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ (/ 0.5 N) N))
0.1b	(/ 0.3333333333333333 (pow N 3))
0.1b	(/ (/ 0.5 N) N)
13.0b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

130×	`times-frac`
94×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
73×	`add-cube-cbrt`
16×	`associate-/l*`
15×	`associate-/r*`
14×	`add-exp-log`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
10×	`div-inv`
6×	`div-exp` `distribute-lft-out--` `difference-of-squares`
5×	`cube-mult`
4×	`pow1` `cbrt-undiv` `unpow3` `frac-add` `distribute-lft-out` `sqr-pow`
2×	`associate-+r+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

66.0ms	(- (/ 1.0 N) (/ (/ 0.5 N) N))
15.0ms	(/ 0.3333333333333333 (pow N 3))
19.0ms	(/ (/ 0.5 N) N)
256.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (/ 1.0 N) (/ (/ 0.5 N) N))
68.0ms	(/ 0.3333333333333333 (pow N 3))
29.0ms	(/ (/ 0.5 N) N)
50.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

simplify2.8s

Counts

195 → 195

Iterations

Iter	Nodes
done	5002
2	4419
1	801
0	316

prune951.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 0.5 N))
0.1b	(/ 0.3333333333333333 (pow N 3))
0.1b	(* (/ 1 N) (- 1.0 (/ 0.5 N)))
13.0b	(+ (/ 0.3333333333333333 (pow N 3)) (* (/ 1 N) (- 1.0 (/ 0.5 N))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
50×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-cube-cbrt`
18×	`add-exp-log`
13×	`associate-l`
12×	`associate-/r*` `unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-r`
5×	`cube-mult` `sub-neg` `flip3--` `div-exp` `frac-add` `flip--`
4×	`distribute-rgt-in` `frac-times` `associate-+r+` `distribute-lft-in` `unpow3` `prod-exp` `associate-*r/` `difference-of-squares` `sqr-pow`
3×	`associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--`
1×	`pow-to-exp` `+-commutative` `rec-exp` `clear-num` `sum-log` `frac-2neg` `flip3-+` `diff-log` `1-exp` `pow-prod-down` `pow-exp` `*-commutative` `flip-+` `distribute-lft-out`

Counts

4 → 147

Calls

4 calls:

9.0ms	(- 1.0 (/ 0.5 N))
7.0ms	(/ 0.3333333333333333 (pow N 3))
77.0ms	(* (/ 1 N) (- 1.0 (/ 0.5 N)))
43.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (/ 1 N) (- 1.0 (/ 0.5 N))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- 1.0 (/ 0.5 N))
40.0ms	(/ 0.3333333333333333 (pow N 3))
101.0ms	(* (/ 1 N) (- 1.0 (/ 0.5 N)))
51.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (/ 1 N) (- 1.0 (/ 0.5 N))))

simplify2.9s

Counts

159 → 159

Iterations

Iter	Nodes
done	5002
2	4891
1	680
0	247

prune550.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes81.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.1b

bsearch46.0ms

Steps

Iters	Range		Point
8	7.674138475383248	27544.66998078673	8020.572324824967

simplify6.0ms

Iterations

Iter	Nodes
done	29
1	29
0	24

end0.0ms

sample2.9s

Algorithm

intervals

Results

793.0ms	1801×	body	1280	valid
681.0ms	4028×	body	80	valid
505.0ms	8152×	body	80	nan
394.0ms	1252×	body	640	valid
115.0ms	629×	body	320	valid
32.0ms	290×	body	160	valid