Details

sample110.0ms

Algorithm

intervals

Results

40.0ms	55×	body	1280	valid
18.0ms	267×	body	80	nan
16.0ms	41×	body	640	valid
14.0ms	133×	body	80	valid
5.0ms	18×	body	320	valid
1.0ms	9×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize22.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (log1p N) (log N))

rewrite12.0ms

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

11.0ms

(- (log1p N) (log N))

series98.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

98.0ms

(- (log1p N) (log N))

simplify1.1s

Counts: 40 → 40

prune383.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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

18.0ms	(/ (+ 1 N) N)
7.0ms	(log (/ (+ 1 N) N))

series115.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

63.0ms	(/ (+ 1 N) N)
51.0ms	(log (/ (+ 1 N) N))

simplify2.0s

Counts: 72 → 72

prune623.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
96×	`times-frac`
85×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
76×	`cbrt-prod`
56×	`log-prod`
54×	`sqrt-prod`
46×	`associate-+r+`
26×	`cbrt-div`
23×	`distribute-lft-out`
16×	`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`
5×	`log-pow`
4×	`expm1-log1p-u` `fma-def` `associate-l/` `associate-r/` `insert-posit16` `log1p-expm1-u` `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 → 246

Calls

4 calls:

Slowest

56.0ms	(+ (log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt N))) (log (/ (cbrt (+ 1 N)) (sqrt N))))
29.0ms	(/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt N))
27.0ms	(* (cbrt (+ 1 N)) (cbrt (+ 1 N)))
15.0ms	(/ (cbrt (+ 1 N)) (sqrt N))

series627.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

358.0ms	(+ (log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt N))) (log (/ (cbrt (+ 1 N)) (sqrt N))))
123.0ms	(/ (cbrt (+ 1 N)) (sqrt N))
96.0ms	(/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (sqrt N))
49.0ms	(* (cbrt (+ 1 N)) (cbrt (+ 1 N)))

simplify1.6s

Counts: 258 → 258

prune3.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (* (log1p N) (log1p N)) (* (log N) (log N)))
0.5b	(* (log N) (log N))
0.3b	(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
0.3b	(* (log1p N) (log1p N))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
29×	`pow1`
27×	`add-cube-cbrt`
20×	`times-frac`
12×	`log-prod`
11×	`log-pow`
10×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
9×	`swap-sqr`
7×	`associate-r` `associate-l` `difference-of-squares`
6×	`distribute-rgt-in` `distribute-lft-in` `associate--r+` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `flip-+` `div-inv`

Counts

4 → 140

Calls

4 calls:

Slowest

25.0ms	(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
13.0ms	(- (* (log1p N) (log1p N)) (* (log N) (log N)))
11.0ms	(* (log1p N) (log1p N))
11.0ms	(* (log N) (log N))

series668.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

269.0ms	(/ (- (* (log1p N) (log1p N)) (* (log N) (log N))) (+ (log1p N) (log N)))
224.0ms	(* (log N) (log N))
118.0ms	(- (* (log1p N) (log1p N)) (* (log N) (log N)))
57.0ms	(* (log1p N) (log1p N))

simplify1.8s

Counts: 152 → 152

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes71.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.3b

bsearch46.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.0s	1746×	body	1280	valid
775.0ms	4128×	body	80	valid
599.0ms	7971×	body	80	nan
460.0ms	1216×	body	640	valid
187.0ms	621×	body	320	valid
43.0ms	289×	body	160	valid