Details

sample116.0ms

Algorithm

intervals

Results

39.0ms	57×	body	1280	valid
22.0ms	288×	body	80	nan
15.0ms	136×	body	80	valid
15.0ms	33×	body	640	valid
7.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid

simplify36.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

36.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize9.0ms

Local error

Found 1 expressions with local error:

2.9b	(- (log1p N) (log N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

Slowest

6.0ms

(- (log1p N) (log N))

series70.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

70.0ms

(- (log1p N) (log N))

simplify2.3s

Counts

38 → 40

Calls

38 calls:

Slowest

213.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
184.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
174.0ms	(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
169.0ms	(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
166.0ms	(fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))

prune359.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

2.9b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite21.0ms

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` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 66

Calls

2 calls:

Slowest

16.0ms	(/ (+ 1 N) N)
4.0ms	(log (/ (+ 1 N) N))

series157.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

84.0ms	(/ (+ 1 N) N)
73.0ms	(log (/ (+ 1 N) N))

simplify1.9s

Counts

57 → 72

Calls

57 calls:

Slowest

327.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
241.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
194.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
137.0ms	(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
116.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune542.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 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))
0.0b	(log (/ 1 (sqrt N)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
102×	`times-frac`
78×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`log-prod`
57×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
16×	`pow1`
15×	`add-exp-log`
14×	`log-pow`
12×	`associate-/r*`
9×	`pow-flip`
8×	`fma-def` `add-cbrt-cube`
7×	`associate-/l*`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `rem-log-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `sqrt-pow1` `pow1/2` `inv-pow`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r-` `sum-log` `log-rec` `associate-+l-`

Counts

4 → 220

Calls

4 calls:

Slowest

21.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
16.0ms	(/ (+ 1 N) (sqrt N))
11.0ms	(/ 1 (sqrt N))
6.0ms	(log (/ 1 (sqrt N)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

216.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
73.0ms	(log (/ 1 (sqrt N)))
56.0ms	(/ (+ 1 N) (sqrt N))
42.0ms	(/ 1 (sqrt N))

simplify4.5s

Counts

214 → 232

Calls

214 calls:

Slowest

340.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* (sqrt N) (sqrt N)) (sqrt N)))
148.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
145.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))
142.0ms	(* (/ 1 (sqrt N)) (/ (+ 1 N) (sqrt N)))
123.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ 1 N) (sqrt N))))

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b	(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ 1 N)))))
0.2b	(/ 1 (/ (sqrt N) (+ 1 N)))
0.2b	(/ 1 (sqrt N))
0.1b	(/ (sqrt N) (+ 1 N))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

408×	`times-frac`
319×	`*-un-lft-identity`
217×	`add-sqr-sqrt` `add-cube-cbrt`
120×	`sqrt-prod`
117×	`log-prod`
95×	`associate-+r+`
55×	`distribute-lft-out`
40×	`associate-/r*`
22×	`associate-+l+`
21×	`add-exp-log`
18×	`associate-/r/`
16×	`pow1`
13×	`add-cbrt-cube` `log-pow`
12×	`div-inv` `associate-/l*`
10×	`div-exp`
9×	`flip3-+` `flip-+` `pow-flip`
8×	`fma-def`
5×	`cbrt-undiv` `inv-pow`
4×	`expm1-log1p-u` `log-rec` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`log-div` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `associate-+r-` `sum-log` `unsub-neg` `associate-+l-` `distribute-neg-out`

Counts

4 → 396

Calls

4 calls:

Slowest

26.0ms	(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ 1 N)))))
13.0ms	(/ 1 (/ (sqrt N) (+ 1 N)))
9.0ms	(/ (sqrt N) (+ 1 N))
5.0ms	(/ 1 (sqrt N))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

287.0ms	(+ (log (/ 1 (sqrt N))) (log (/ 1 (/ (sqrt N) (+ 1 N)))))
67.0ms	(/ (sqrt N) (+ 1 N))
61.0ms	(/ 1 (/ (sqrt N) (+ 1 N)))
29.0ms	(/ 1 (sqrt N))

simplify24.1s

Counts

478 → 408

Calls

478 calls:

Slowest

571.0ms	(/ (* (* 1 1) 1) (/ (* (* (sqrt N) (sqrt N)) (sqrt N)) (* (* (+ 1 N) (+ 1 N)) (+ 1 N))))
459.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt N) (+ (pow 1 3) (pow N 3))))
448.0ms	(/ 1 (/ (sqrt N) (+ (pow 1 3) (pow N 3))))
369.0ms	(log (/ 1 (cbrt (/ (sqrt N) (+ 1 N)))))
356.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt N)) (cbrt (sqrt N))) (* (cbrt (+ 1 N)) (cbrt (+ 1 N)))))

prune4.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch32.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	1744×	body	1280	valid
953.0ms	8044×	body	80	nan
482.0ms	1261×	body	640	valid
453.0ms	4102×	body	80	valid
145.0ms	590×	body	320	valid
51.0ms	303×	body	160	valid