Details

sample66.0ms

Algorithm

intervals

Results

20.0ms	54×	body	1280	valid
10.0ms	42×	body	640	valid
8.0ms	130×	body	80	valid
8.0ms	223×	body	80	nan
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

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

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

28.0ms	(- (log (+ N 1.0)) (log N))
6.0ms	(log (+ N 1.0))

series212.0ms

Counts

2 → 6

Calls

2 calls:

159.0ms	(- (log (+ N 1.0)) (log N))
53.0ms	(log (+ N 1.0))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	127	1052
1	288	863
2	1086	705
done	5001	614

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite60.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
10.0ms	(log (/ (+ N 1.0) N))

series195.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(/ (+ N 1.0) N)
104.0ms	(log (/ (+ N 1.0) N))

simplify834.0ms

Counts

70 → 70

Iterations

Useful iterations: done (830.0ms)

Iter	Nodes	Cost
0	112	749
1	253	708
2	1053	660
done	5000	647

prune168.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

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)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
42×	`times-frac`
39×	`log-prod`
38×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`sqrt-prod`
25×	`associate-+r+`
13×	`distribute-lft-out`
11×	`pow1`
10×	`log-pow`
7×	`associate-+l+` `associate-/l*`
6×	`add-exp-log` `fma-def` `sqrt-div`
5×	`log-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

3 → 127

Calls

3 calls:

16.0ms	(/ (sqrt (+ N 1.0)) N)
31.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
11.0ms	(log (sqrt (+ N 1.0)))

series550.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (sqrt (+ N 1.0)) N)
323.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
122.0ms	(log (sqrt (+ N 1.0)))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	222	1816
1	484	1663
2	1790	1530
done	5001	1506

prune422.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize42.0ms

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))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

196×	`prod-diff`
140×	`unpow-prod-down` `cube-prod`
118×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
81×	`pow1`
77×	`log-pow`
37×	`sqr-pow`
29×	`cube-mult` `unpow3`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 309

Calls

4 calls:

64.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
10.0ms	(log (+ N 1.0))
9.0ms	(log (+ N 1.0))
9.0ms	(log (+ N 1.0))

series499.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
66.0ms	(log (+ N 1.0))
74.0ms	(log (+ N 1.0))
60.0ms	(log (+ N 1.0))

simplify3.0s

Counts

321 → 321

Iterations

Useful iterations: 2 (732.0ms)

Iter	Nodes	Cost
0	323	11205
1	827	6777
2	3817	5125
done	5000	5125

prune607.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes71.0ms

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

sample2.6s

Algorithm

intervals

Results

920.0ms	1817×	body	1280	valid
406.0ms	1308×	body	640	valid
382.0ms	7921×	body	80	nan
286.0ms	3980×	body	80	valid
145.0ms	593×	body	320	valid
75.0ms	302×	body	160	valid