Details

sample117.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
23.0ms	24×	body	320	valid
22.0ms	52×	body	640	valid
11.0ms	165×	body	80	valid
6.0ms	110×	body	80	nan
2.0ms	12×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	107	9
5	245	9
6	580	9
7	1850	9
done	5000	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.4b	(pow (/ x (+ x y)) x)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

43.0ms	(/ (pow (/ x (+ x y)) x) x)
11.0ms	(/ x (+ x y))
19.0ms	(pow (/ x (+ x y)) x)

series531.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(/ (pow (/ x (+ x y)) x) x)
62.0ms	(/ x (+ x y))
292.0ms	(pow (/ x (+ x y)) x)

simplify1.5s

Counts

187 → 187

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	282	2929
1	545	2745
2	1552	2688
done	5000	2684

prune587.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (- y)) x)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

28.0ms

(/ (exp (- y)) x)

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(/ (exp (- y)) x)

simplify2.7s

Counts

34 → 34

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	66	311
1	120	300
2	293	280
3	709	278
4	2815	278
done	5002	278

prune99.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
0.6b	(cbrt (+ x y))
2.0b	(pow (/ x (cbrt (+ x y))) x)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
27×	`unpow-prod-down`
24×	`cbrt-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
8×	`cbrt-div`
7×	`add-exp-log`
6×	`distribute-lft-out`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`pow-exp` `associate-/r/`
1×	`pow-to-exp` `pow-pow` `div-exp` `div-inv` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

8.0ms	(cbrt (+ x y))
8.0ms	(cbrt (+ x y))
8.0ms	(cbrt (+ x y))
31.0ms	(pow (/ x (cbrt (+ x y))) x)

series748.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt (+ x y))
202.0ms	(cbrt (+ x y))
232.0ms	(cbrt (+ x y))
131.0ms	(pow (/ x (cbrt (+ x y))) x)

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	211	1435
1	513	1331
2	1333	1297
3	4422	1279
done	5000	1279

prune510.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x y))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`cbrt-prod`
10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div`
1×	`flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

4.0ms	(cbrt (+ x y))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.0s

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (+ x y))
301.0ms	(cbrt x)
295.0ms	(cbrt x)
271.0ms	(cbrt x)

simplify2.4s

Counts

67 → 67

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	73	384
1	151	361
2	329	335
3	729	322
4	2012	322
done	5001	320

prune429.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes70.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 11.2b

bsearch104.0ms

Steps

Iters	Range		Point
8	0.00013312118248051433	0.12160444842987421	0.12040142811151512
7	-123.41774798665298	-0.7718806003288846	-10.119424086535442

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	28	64
1	36	60
done	36	60

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1549×	body	1280	valid
720.0ms	3131×	body	80	nan
709.0ms	1489×	body	640	valid
399.0ms	4811×	body	80	valid
220.0ms	839×	body	320	valid
72.0ms	446×	body	160	valid