Details

sample83.0ms

Algorithm

intervals

Results

29.0ms	55×	body	1280	valid
14.0ms	267×	body	80	nan
12.0ms	41×	body	640	valid
10.0ms	133×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize23.0ms

Local error

Found 2 expressions with local error:

3.3b	(log (+ N 1))
2.8b	(- (log (+ N 1)) (log N))

rewrite12.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

Slowest

8.0ms	(- (log (+ N 1)) (log N))
3.0ms	(log (+ N 1))

series125.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

92.0ms	(- (log (+ N 1)) (log N))
33.0ms	(log (+ N 1))

simplify1.1s

Counts: 49 → 49

prune631.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 2 expressions with local error:

3.3b	(log (/ (+ N 1) N))
0.0b	(/ (+ N 1) N)

rewrite34.0ms

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` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

Slowest

26.0ms	(/ (+ N 1) N)
7.0ms	(log (/ (+ N 1) N))

series142.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

71.0ms	(/ (+ N 1) N)
71.0ms	(log (/ (+ N 1) N))

simplify2.2s

Counts: 68 → 68

prune564.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

3.5b	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))
0.3b	(/ (cbrt (+ N 1)) (sqrt N))
0.3b	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
0.3b	(* (cbrt (+ N 1)) (cbrt (+ N 1)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

120×	`*-un-lft-identity`
96×	`times-frac`
84×	`add-sqr-sqrt`
76×	`cbrt-prod` `add-cube-cbrt`
56×	`log-prod`
54×	`sqrt-prod`
46×	`associate-+r+`
26×	`cbrt-div`
23×	`distribute-lft-out`
15×	`pow1`
14×	`flip3-+` `flip-+`
13×	`add-exp-log`
12×	`associate-/r*`
10×	`associate-+l+` `associate-/l/`
9×	`swap-sqr`
8×	`frac-times` `add-cbrt-cube` `associate-/l*`
7×	`associate-r` `associate-l`
6×	`pow1/3`
4×	`associate-l/` `associate-r/` `log-pow` `insert-posit16` `div-inv` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`log-div` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `pow-sqr` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `+-commutative` `associate-+r-` `sum-log` `pow-plus` `*-commutative` `associate-+l-`

Counts

4 → 234

Calls

4 calls:

Slowest

60.0ms	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))
43.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
21.0ms	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
10.0ms	(/ (cbrt (+ N 1)) (sqrt N))

series696.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

381.0ms	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))
132.0ms	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
115.0ms	(/ (cbrt (+ N 1)) (sqrt N))
67.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))

simplify1.8s

Counts: 246 → 246

prune3.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ 1 (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (+ N 1)) (cbrt (sqrt N)))))
0.6b	(cbrt (sqrt N))
0.6b	(cbrt (sqrt N))
0.6b	(cbrt (sqrt N))

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
83×	`*-un-lft-identity`
67×	`associate-+r+` `log-prod`
63×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`sqrt-prod`
27×	`distribute-lft-out`
17×	`pow1`
13×	`log-pow`
5×	`associate-+l-` `add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`log-div` `sum-log` `pow1/3`
2×	`associate-+r-` `log-rec`
1×	`+-commutative` `associate-+l+` `flip3-+` `unsub-neg` `flip-+` `div-inv`

Counts

4 → 141

Calls

4 calls:

Slowest

463.0ms	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ 1 (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (+ N 1)) (cbrt (sqrt N)))))
2.0ms	(cbrt (sqrt N))
2.0ms	(cbrt (sqrt N))
2.0ms	(cbrt (sqrt N))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

470.0ms	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ 1 (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (+ N 1)) (cbrt (sqrt N)))))
287.0ms	(cbrt (sqrt N))
249.0ms	(cbrt (sqrt N))
204.0ms	(cbrt (sqrt N))

simplify1.2s

Counts: 153 → 153

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes156.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch64.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	7971×	body	80	nan
997.0ms	1746×	body	1280	valid
471.0ms	1216×	body	640	valid
395.0ms	4128×	body	80	valid
190.0ms	621×	body	320	valid
46.0ms	289×	body	160	valid