Details

sample112.0ms

Algorithm

intervals

Results

37.0ms	60×	body	1280	valid
21.0ms	267×	body	80	nan
17.0ms	42×	body	640	valid
12.0ms	115×	body	80	valid
8.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	13
2	13
1	11
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize9.0ms

Local error

Found 1 expressions with local error:

3.4b	(- (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:

7.0ms

(- (log1p N) (log N))

series130.0ms

Counts

1 → 3

Calls

1 calls:

130.0ms

(- (log1p N) (log N))

simplify2.2s

Counts

40 → 40

Iterations

Iter	Nodes
4	2841
3	991
2	370
1	185
0	83

prune385.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) (* N N))
10.2b	(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

rewrite32.0ms

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:

1.0ms	(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
16.0ms	(/ (/ 1 N) N)
10.0ms	(/ (/ 1 N) (* N N))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
30.0ms	(/ (/ 1 N) N)
59.0ms	(/ (/ 1 N) (* N N))
37.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

simplify4.3s

Counts

172 → 172

Iterations

Iter	Nodes
3	6069
2	1365
1	533
0	235

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 N) N)
0.1b	(* (/ (/ 1 N) N) (/ 1 N))
2.3b	(log (exp (* (/ (/ 1 N) N) (/ 1 N))))
10.2b	(fma (/ (/ 1 N) N) -1/2 (fma (log (exp (* (/ (/ 1 N) N) (/ 1 N)))) 1/3 (/ 1 N)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

175×	`times-frac`
133×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
89×	`add-cube-cbrt`
78×	`add-exp-log`
43×	`associate-l`
40×	`div-exp`
30×	`add-cbrt-cube`
20×	`prod-exp`
18×	`pow1`
15×	`unswap-sqr`
14×	`div-inv`
13×	`associate-r` `associate-/l*`
12×	`cbrt-undiv`
10×	`rec-exp` `1-exp`
6×	`cbrt-unprod` `pow-div`
5×	`pow-flip` `inv-pow` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-up` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-/r*` `log-pow`
1×	`frac-times` `exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `rem-log-exp` `pow3` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

10.0ms	(/ (/ 1 N) N)
35.0ms	(* (/ (/ 1 N) N) (/ 1 N))
8.0ms	(log (exp (* (/ (/ 1 N) N) (/ 1 N))))
1.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (log (exp (* (/ (/ 1 N) N) (/ 1 N)))) 1/3 (/ 1 N)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (/ 1 N) N)
37.0ms	(* (/ (/ 1 N) N) (/ 1 N))
60.0ms	(log (exp (* (/ (/ 1 N) N) (/ 1 N))))
29.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (log (exp (* (/ (/ 1 N) N) (/ 1 N)))) 1/3 (/ 1 N)))

simplify806.0ms

Counts

235 → 235

Iterations

Iter	Nodes
2	2079
1	823
0	288

prune2.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 N) N)
0.1b	(/ (/ 1 N) N)
0.1b	(* (/ (/ 1 N) N) (/ 1 N))
10.2b	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ (/ 1 N) N) (/ 1 N)) 1/3 (/ 1 N)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

250×	`times-frac`
174×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
130×	`add-cube-cbrt`
87×	`add-exp-log`
46×	`div-exp`
43×	`associate-l`
35×	`add-cbrt-cube`
26×	`associate-/l*`
20×	`pow1` `prod-exp`
19×	`div-inv`
15×	`cbrt-undiv` `unswap-sqr`
13×	`associate-r`
11×	`rec-exp` `1-exp`
8×	`pow-div`
6×	`associate-/r*` `cbrt-unprod` `pow-flip` `inv-pow`
4×	`expm1-log1p-u` `pow-prod-up` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `pow3` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 283

Calls

4 calls:

16.0ms	(/ (/ 1 N) N)
16.0ms	(/ (/ 1 N) N)
19.0ms	(* (/ (/ 1 N) N) (/ 1 N))
0.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ (/ 1 N) N) (/ 1 N)) 1/3 (/ 1 N)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (/ 1 N) N)
32.0ms	(/ (/ 1 N) N)
63.0ms	(* (/ (/ 1 N) N) (/ 1 N))
55.0ms	(fma (/ (/ 1 N) N) -1/2 (fma (* (/ (/ 1 N) N) (/ 1 N)) 1/3 (/ 1 N)))

simplify835.0ms

Counts

295 → 295

Iterations

Iter	Nodes
2	2181
1	810
0	270

prune2.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch43.0ms

Steps

Iters	Range		Point
8	9369.000823706243	5623247.098758675	9516.15297930401

simplify2.0ms

Iterations

Iter	Nodes
2	19
1	19
0	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	1817×	body	1280	valid
649.0ms	8102×	body	80	nan
494.0ms	1222×	body	640	valid
390.0ms	4055×	body	80	valid
154.0ms	609×	body	320	valid
49.0ms	297×	body	160	valid