Details

sample60.0ms

Algorithm

intervals

Results

19.0ms	67×	body	640	valid
9.0ms	124×	body	80	valid
7.0ms	20×	body	1280	valid
7.0ms	31×	body	320	valid
2.0ms	14×	body	160	valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

9.0ms	(/ 1.0 (+ x 1.0))
10.0ms	(/ 1.0 (- x 1.0))
84.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
356.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (+ x 1.0))
35.0ms	(/ 1.0 (- x 1.0))
72.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
708.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.6s

Counts

630 → 630

Iterations

Iter	Nodes
done	5000
2	4188
1	1192
0	501

prune3.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7)))
0.1b	(/ (/ 2.0 x) (* x x))
0.2b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

95×	`times-frac`
60×	`*-un-lft-identity`
58×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`add-exp-log`
24×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`associate-/l*`
17×	`fma-def`
15×	`associate-/r*`
12×	`div-exp`
8×	`cbrt-undiv` `sqr-pow`
7×	`div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`pow-to-exp` `pow-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

84.0ms	(+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7)))
11.0ms	(/ (/ 2.0 x) (* x x))
6.0ms	(/ 2.0 (pow x 7))
14.0ms	(/ 2.0 (pow x 5))

series492.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7)))
71.0ms	(/ (/ 2.0 x) (* x x))
97.0ms	(/ 2.0 (pow x 7))
63.0ms	(/ 2.0 (pow x 5))

simplify1.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
2	2803
1	602
0	269

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 2.0 x) x) x)
0.1b	(/ (/ 2.0 x) x)
0.2b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 5))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

510×	`times-frac`
262×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
62×	`associate-/l*`
28×	`add-exp-log`
24×	`unpow-prod-down` `div-inv`
22×	`add-cbrt-cube`
20×	`associate-/r*`
15×	`div-exp`
11×	`cbrt-undiv`
8×	`sqr-pow`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `associate-/l/`

Counts

4 → 360

Calls

4 calls:

23.0ms	(/ (/ (/ 2.0 x) x) x)
12.0ms	(/ (/ 2.0 x) x)
11.0ms	(/ 2.0 (pow x 7))
11.0ms	(/ 2.0 (pow x 5))

series265.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (/ (/ 2.0 x) x) x)
33.0ms	(/ (/ 2.0 x) x)
80.0ms	(/ 2.0 (pow x 7))
99.0ms	(/ 2.0 (pow x 5))

simplify1.1s

Counts

372 → 372

Iterations

Iter	Nodes
done	5000
1	1315
0	562

prune2.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (/ 2.0 x) x)) (sqrt (/ (/ 2.0 x) x)))
0.3b	(/ 2.0 (pow x 5))
30.3b	(sqrt (/ (/ 2.0 x) x))
30.3b	(sqrt (/ (/ 2.0 x) x))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

447×	`times-frac`
306×	`add-sqr-sqrt`
284×	`sqrt-prod`
234×	`*-un-lft-identity` `add-cube-cbrt`
48×	`swap-sqr`
46×	`associate-r` `associate-l`
25×	`div-inv`
21×	`pow1`
16×	`unswap-sqr`
12×	`unpow-prod-down`
11×	`add-exp-log`
10×	`sqrt-pow1` `pow1/2`
8×	`add-cbrt-cube`
7×	`associate-/r*`
6×	`rem-sqrt-square` `sqrt-div`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`div-exp` `pow-prod-down` `pow-sqr` `associate-/l*`
1×	`pow2` `frac-times` `pow-to-exp` `cbrt-undiv` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-l/` `pow-exp` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 349

Calls

4 calls:

90.0ms	(* (sqrt (/ (/ 2.0 x) x)) (sqrt (/ (/ 2.0 x) x)))
14.0ms	(/ 2.0 (pow x 5))
8.0ms	(sqrt (/ (/ 2.0 x) x))
8.0ms	(sqrt (/ (/ 2.0 x) x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (sqrt (/ (/ 2.0 x) x)) (sqrt (/ (/ 2.0 x) x)))
84.0ms	(/ 2.0 (pow x 5))
52.0ms	(sqrt (/ (/ 2.0 x) x))
70.0ms	(sqrt (/ (/ 2.0 x) x))

simplify2.3s

Counts

361 → 361

Iterations

Iter	Nodes
done	5000
2	3593
1	826
0	460

prune2.4s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes171.0ms

Accuracy

90.7% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 9.6b

bsearch3.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	34
1	34
0	29

end0.0ms

sample1.8s

Algorithm

intervals

Results

678.0ms	568×	body	1280	valid
467.0ms	1803×	body	640	valid
291.0ms	4238×	body	80	valid
188.0ms	951×	body	320	valid
48.0ms	440×	body	160	valid