Details

sample97.0ms

Algorithm

intervals

Results

29.0ms	56×	body	1280	valid
14.0ms	288×	body	80	nan
13.0ms	142×	body	80	valid
10.0ms	31×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize19.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite51.0ms

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:

42.0ms	(- (log (+ N 1.0)) (log N))
8.0ms	(log (+ N 1.0))

series225.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(- (log (+ N 1.0)) (log N))
77.0ms	(log (+ N 1.0))

simplify1.2s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	2789
2	645
1	213
0	101

prune220.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 N) N)
3.3b	(log (/ (+ 1.0 N) N))

rewrite31.0ms

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:

20.0ms	(/ (+ 1.0 N) N)
9.0ms	(log (/ (+ 1.0 N) N))

series209.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (+ 1.0 N) N)
138.0ms	(log (/ (+ 1.0 N) N))

simplify493.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	1011
1	243
0	107

prune244.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (pow (log (+ 1.0 N)) 3) (pow (log N) 3))
3.2b	(log (+ 1.0 N))
3.2b	(log (+ 1.0 N))
3.2b	(log (+ 1.0 N))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
23×	`pow1`
19×	`log-pow`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
12×	`log-prod`
8×	`sqr-pow`
7×	`add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 91

Calls

4 calls:

40.0ms	(- (pow (log (+ 1.0 N)) 3) (pow (log N) 3))
7.0ms	(log (+ 1.0 N))
7.0ms	(log (+ 1.0 N))
5.0ms	(log (+ 1.0 N))

series428.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(- (pow (log (+ 1.0 N)) 3) (pow (log N) 3))
48.0ms	(log (+ 1.0 N))
53.0ms	(log (+ 1.0 N))
49.0ms	(log (+ 1.0 N))

simplify882.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	2098
1	483
0	192

prune597.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ 0.5 (* N N))
0.3b	(/ 0.3333333333333333 (pow N 3))
19.1b	(- (/ 0.5 (* N N)) (/ 0.3333333333333333 (pow N 3)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
54×	`times-frac`
34×	`*-un-lft-identity`
30×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-/r*` `add-exp-log`
10×	`add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*` `sqr-pow`
5×	`cube-mult` `div-exp` `add-log-exp`
4×	`unpow3`
3×	`pow1` `cbrt-undiv`
2×	`clear-num` `frac-2neg` `div-inv` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `prod-exp` `frac-sub` `cbrt-unprod` `flip--`

Counts

3 → 111

Calls

3 calls:

9.0ms	(/ 0.5 (* N N))
6.0ms	(/ 0.3333333333333333 (pow N 3))
72.0ms	(- (/ 0.5 (* N N)) (/ 0.3333333333333333 (pow N 3)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 0.5 (* N N))
60.0ms	(/ 0.3333333333333333 (pow N 3))
113.0ms	(- (/ 0.5 (* N N)) (/ 0.3333333333333333 (pow N 3)))

simplify1.9s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	3228
1	437
0	175

prune441.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch60.0ms

Steps

Iters	Range		Point
8	5.1212688054922095	43837.056983701754	7426.10510392418

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

723.0ms	1688×	body	1280	valid
482.0ms	7906×	body	80	nan
406.0ms	4067×	body	80	valid
353.0ms	1295×	body	640	valid
119.0ms	668×	body	320	valid
68.0ms	282×	body	160	valid