Details

sample99.0ms

Algorithm

intervals

Results

28.0ms	48×	body	1280	valid
20.0ms	50×	body	640	valid
18.0ms	274×	body	80	nan
12.0ms	128×	body	80	valid
5.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify26.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

25.0ms

(- (log (+ N 1)) (log N))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize12.0ms

Local error

Found 2 expressions with local error:

2.7b	(log (+ N 1))
2.5b	(- (log (+ N 1)) (log N))

rewrite13.0ms

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

9.0ms	(- (log (+ N 1)) (log N))
3.0ms	(log (+ N 1))

series113.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

86.0ms	(- (log (+ N 1)) (log N))
26.0ms	(log (+ N 1))

simplify2.9s

Counts

57 → 49

Calls

57 calls:

Slowest

388.0ms	(* (* (- (log (+ N 1)) (log N)) (- (log (+ N 1)) (log N))) (- (log (+ N 1)) (log N)))
382.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
255.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
206.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
176.0ms	(- (pow (log (+ N 1)) 3) (pow (log N) 3))

prune394.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite29.0ms

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

15.0ms	(/ (+ 1 N) N)
13.0ms	(log (/ (+ 1 N) N))

series105.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

61.0ms	(/ (+ 1 N) N)
44.0ms	(log (/ (+ 1 N) N))

simplify3.8s

Counts

96 → 68

Calls

96 calls:

Slowest

429.0ms	(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
375.0ms	(* (* (/ (+ 1 N) N) (/ (+ 1 N) N)) (/ (+ 1 N) N))
329.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
277.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
223.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune528.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

2.9b	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
0.4b	(/ (+ 1 N) (sqrt N))
0.2b	(/ 1 (sqrt N))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
84×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt`
50×	`log-prod`
48×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
12×	`associate-/r*`
9×	`pow1` `add-exp-log`
7×	`add-cbrt-cube` `associate-/l*`
4×	`log-pow` `div-inv`
3×	`div-exp` `insert-posit16` `pow-flip` `add-log-exp`
2×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `rec-exp` `associate-+r-` `sum-log` `sqrt-pow1` `pow1/2` `1-exp` `associate-+l-` `inv-pow`

Counts

3 → 163

Calls

3 calls:

Slowest

28.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
18.0ms	(/ (+ 1 N) (sqrt N))
5.0ms	(/ 1 (sqrt N))

series349.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

228.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
73.0ms	(/ (+ 1 N) (sqrt N))
48.0ms	(/ 1 (sqrt N))

simplify14.7s

Counts

216 → 172

Calls

216 calls:

Slowest

803.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt (sqrt N)))))
724.0ms	(* (* (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N)))) (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))) (+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N)))))
405.0ms	(+ (* (log (/ 1 (sqrt N))) (log (/ 1 (sqrt N)))) (- (* (log (/ (+ 1 N) (sqrt N))) (log (/ (+ 1 N) (sqrt N)))) (* (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))))
389.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt (* (cbrt N) (cbrt N))))))
381.0ms	(* (* (/ (+ 1 N) (sqrt N)) (/ (+ 1 N) (sqrt N))) (/ (+ 1 N) (sqrt N)))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

2.7b	(log (/ (sqrt (+ 1 N)) 1))
2.7b	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
0.2b	(/ (sqrt (+ 1 N)) N)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
84×	`times-frac`
75×	`log-prod`
61×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`sqrt-prod`
25×	`associate-+l+` `associate-+r+`
17×	`distribute-lft-out`
9×	`add-exp-log`
8×	`pow1`
7×	`associate-/l*`
5×	`add-cbrt-cube` `log-pow`
4×	`div-inv`
3×	`log-div` `associate-/r*` `div-exp` `rem-log-exp` `insert-posit16` `add-log-exp`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `1-exp` `associate-+l-`

Counts

3 → 152

Calls

3 calls:

Slowest

19.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
10.0ms	(/ (sqrt (+ 1 N)) N)
7.0ms	(log (/ (sqrt (+ 1 N)) 1))

series383.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

220.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))
87.0ms	(/ (sqrt (+ 1 N)) N)
77.0ms	(log (/ (sqrt (+ 1 N)) 1))

simplify15.7s

Counts

207 → 161

Calls

207 calls:

Slowest

1.1s	(* (* (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N))) (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))) (+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N))))
396.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (* (cbrt (+ 1 N)) (cbrt (+ 1 N)))) (* (cbrt N) (cbrt N)))))
375.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (sqrt (+ 1 N))) (* (cbrt N) (cbrt N)))))
373.0ms	(/ (* (* (sqrt (+ 1 N)) (sqrt (+ 1 N))) (sqrt (+ 1 N))) (* (* N N) N))
340.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (sqrt (+ 1 N))) (* (cbrt N) (cbrt N)))))

prune1.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.7b

bsearch74.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

958.0ms	1697×	body	1280	valid
803.0ms	4173×	body	80	valid
703.0ms	8167×	body	80	nan
484.0ms	1216×	body	640	valid
184.0ms	632×	body	320	valid
46.0ms	282×	body	160	valid