Details

sample73.0ms

Algorithm

intervals

Results

21.0ms	54×	body	1280	valid
11.0ms	42×	body	640	valid
9.0ms	223×	body	80	nan
9.0ms	130×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize14.0ms

Local error

Found 2 expressions with local error:

3.0b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
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:

17.0ms	(- (log (+ N 1.0)) (log N))
10.0ms	(log (+ N 1.0))

series201.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(- (log (+ N 1.0)) (log N))
76.0ms	(log (+ N 1.0))

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	643	445
3	2849	443
done	5001	438

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.1b	(log (/ (+ N 1.0) N))

rewrite65.0ms

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` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

41.0ms	(/ (+ N 1.0) N)
18.0ms	(log (/ (+ N 1.0) N))

series210.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (+ N 1.0) N)
145.0ms	(log (/ (+ N 1.0) N))

simplify608.0ms

Counts

66 → 66

Iterations

Useful iterations: done (606.0ms)

Iter	Nodes	Cost
0	108	723
1	243	690
2	1010	637
done	5000	624

prune144.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) N)
3.0b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.2b	(log (sqrt (+ N 1.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
42×	`times-frac`
39×	`log-prod`
37×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`sqrt-prod`
25×	`associate-+r+`
13×	`distribute-lft-out`
9×	`pow1`
7×	`associate-+l+` `log-pow` `associate-/l*`
6×	`add-exp-log` `sqrt-div`
5×	`log-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`associate-/r*` `add-log-exp`
2×	`associate-+l-` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

3 → 115

Calls

3 calls:

18.0ms	(/ (sqrt (+ N 1.0)) N)
43.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
6.0ms	(log (sqrt (+ N 1.0)))

series557.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (sqrt (+ N 1.0)) N)
310.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
122.0ms	(log (sqrt (+ N 1.0)))

simplify993.0ms

Counts

124 → 124

Iterations

Useful iterations: done (987.0ms)

Iter	Nodes	Cost
0	216	1762
1	466	1615
2	1723	1490
done	5000	1464

prune394.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

3.0b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))

rewrite97.0ms

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:

65.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
9.0ms	(log (+ N 1.0))
9.0ms	(log (+ N 1.0))
10.0ms	(log (+ N 1.0))

series430.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
44.0ms	(log (+ N 1.0))
76.0ms	(log (+ N 1.0))
55.0ms	(log (+ N 1.0))

simplify1.2s

Counts

103 → 103

Iterations

Useful iterations: 2 (357.0ms)

Iter	Nodes	Cost
0	193	1673
1	481	1563
2	2111	1497
done	5003	1497

prune423.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.1b

bsearch45.0ms

Steps

Iters	Range		Point
9	7337.051904760935	2116652649.122401	11281.627494186123

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	25
1	20	25
done	20	25

end0.0ms

sample2.8s

Algorithm

intervals

Results

826.0ms	1817×	body	1280	valid
821.0ms	7921×	body	80	nan
317.0ms	3980×	body	80	valid
315.0ms	1308×	body	640	valid
94.0ms	593×	body	320	valid
34.0ms	302×	body	160	valid