Details

sample118.0ms

Algorithm

intervals

Results

42.0ms	62×	body	1280	valid
21.0ms	270×	body	80	nan
15.0ms	34×	body	640	valid
14.0ms	125×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize11.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (log1p N) (log N))

rewrite8.0ms

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

7.0ms

(- (log1p N) (log N))

series96.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

96.0ms

(- (log1p N) (log N))

simplify1.6s

Counts: 40 → 40

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

12.2b	(fma (/ (/ 1 N) N) -1/2 (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) (* N N))
0.0b	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
60×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
35×	`add-exp-log`
26×	`associate-/l*`
21×	`pow1` `add-cbrt-cube`
18×	`div-exp`
10×	`pow-div`
9×	`cbrt-undiv`
8×	`div-inv`
5×	`pow-flip` `inv-pow`
4×	`expm1-log1p-u` `associate-/r*` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `cbrt-unprod` `fma-udef` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

Slowest

16.0ms	(/ (/ 1 N) (* N N))
7.0ms	(/ (/ 1 N) N)
0.0ms	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

122.0ms	(fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))
71.0ms	(/ (/ 1 N) (* N N))
45.0ms	(fma (/ (/ 1 N) N) -1/2 (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
35.0ms	(/ (/ 1 N) N)

simplify2.2s

Counts: 172 → 172

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

19.9b	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
19.9b	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
19.9b	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
12.2b	(fma (/ (/ 1 N) N) -1/2 (* (* (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

Slowest

1.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
1.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
1.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (* (* (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

171.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
154.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
151.0ms	(cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))
27.0ms	(fma (/ (/ 1 N) N) -1/2 (* (* (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))) (cbrt (fma 1/3 (/ (/ 1 N) (* N N)) (/ 1 N)))))

simplify1.9s

Counts: 65 → 65

prune730.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

3.7b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite37.0ms

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

27.0ms	(/ (+ 1 N) N)
8.0ms	(log (/ (+ 1 N) N))

series121.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(/ (+ 1 N) N)
59.0ms	(log (/ (+ 1 N) N))

simplify1.6s

Counts: 72 → 72

prune566.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.5b

bsearch64.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.4s	1805×	body	1280	valid
529.0ms	8156×	body	80	nan
487.0ms	4022×	body	80	valid
404.0ms	1171×	body	640	valid
178.0ms	645×	body	320	valid
55.0ms	357×	body	160	valid