Details

sample92.0ms

Algorithm

intervals

Results

46.0ms	106×	body	1280	valid
20.0ms	84×	body	640	valid
6.0ms	238×	body	80	nan
5.0ms	39×	body	320	valid
2.0ms	21×	body	160	valid
0.0ms	6×	body	80	valid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	18	12
2	25	12
3	40	12
4	65	12
5	96	12
6	118	12
7	126	12
8	128	12
done	128	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 x) (- 1.0 x))
6.5b	(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/r*`
4×	`associate-/r/` `add-cbrt-cube` `associate-/l*`
3×	`pow1`
2×	`expm1-log1p-u` `flip3--` `div-exp` `rem-log-exp` `flip--` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 86

Calls

2 calls:

23.0ms	(/ (+ 1.0 x) (- 1.0 x))
10.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

series147.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (+ 1.0 x) (- 1.0 x))
116.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	146	1310
1	335	1243
2	851	1182
3	2166	1136
done	5000	1134

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune4.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (log (sqrt (- 1.0 x)))) (log (/ (+ 1.0 x) (sqrt (- 1.0 x)))))
0.0b	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
6.4b	(log (sqrt (- 1.0 x)))
6.5b	(log (/ (+ 1.0 x) (sqrt (- 1.0 x))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
96×	`times-frac`
94×	`add-sqr-sqrt`
92×	`log-prod`
75×	`sqrt-prod`
64×	`add-cube-cbrt`
38×	`associate-+r+`
31×	`distribute-lft-out`
16×	`pow1` `fma-def`
15×	`log-pow` `distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `distribute-rgt-neg-in`
8×	`associate-+l+` `distribute-neg-in` `sqrt-div` `associate-/r*`
6×	`distribute-lft-neg-in` `associate-/r/` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-div` `flip3--` `flip--` `log1p-expm1-u` `associate-/l*`
3×	`sqrt-pow1` `pow1/2` `rem-log-exp` `div-inv`
2×	`flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `associate-+r-` `neg-mul-1` `frac-2neg` `neg-log` `clear-num`

Counts

4 → 220

Calls

4 calls:

39.0ms	(+ (- (log (sqrt (- 1.0 x)))) (log (/ (+ 1.0 x) (sqrt (- 1.0 x)))))
28.0ms	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
6.0ms	(log (sqrt (- 1.0 x)))
11.0ms	(log (/ (+ 1.0 x) (sqrt (- 1.0 x))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(+ (- (log (sqrt (- 1.0 x)))) (log (/ (+ 1.0 x) (sqrt (- 1.0 x)))))
84.0ms	(/ (+ 1.0 x) (sqrt (- 1.0 x)))
78.0ms	(log (sqrt (- 1.0 x)))
184.0ms	(log (/ (+ 1.0 x) (sqrt (- 1.0 x))))

simplify952.0ms

Counts

232 → 232

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	304	3749
1	687	3450
2	1990	3187
done	5000	2968

prune467.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
0.0b	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
6.6b	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))
6.6b	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

286×	`sqrt-prod`
262×	`*-un-lft-identity`
224×	`times-frac`
194×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
124×	`log-prod`
34×	`distribute-lft-out`
30×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r*`
14×	`add-exp-log` `associate-/l*`
12×	`sqrt-div`
8×	`associate-/r/` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `flip3--` `div-exp` `rem-log-exp` `flip--` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `log-div` `sqrt-undiv` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

4 → 330

Calls

4 calls:

26.0ms	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
23.0ms	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
13.0ms	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))
13.0ms	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
86.0ms	(/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x)))
175.0ms	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))
178.0ms	(log (/ (sqrt (+ 1.0 x)) (sqrt (- 1.0 x))))

simplify1.6s

Counts

342 → 342

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	247	6854
1	510	6106
2	1192	5908
3	3043	5732
done	5000	5712

prune592.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes17.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
done	14	20

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	3418×	body	1280	valid
600.0ms	2486×	body	640	valid
213.0ms	7910×	body	80	nan
182.0ms	1232×	body	320	valid
56.0ms	649×	body	160	valid
11.0ms	215×	body	80	valid