Details

sample116.0ms

Algorithm

intervals

Results

39.0ms	48×	body	1280	valid
29.0ms	57×	body	640	valid
14.0ms	157×	body	80	valid
10.0ms	32×	body	320	valid
8.0ms	113×	body	80	nan
2.0ms	8×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1916
6	531
5	212
4	89
3	41
2	22
1	15
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.4b	(log (/ x (+ x y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`associate-/r` `flip3-+` `associate-r*` `flip-+` `div-inv`
3×	`associate-l` `insert-posit16` `associate-/l*` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 120

Calls

3 calls:

20.0ms	(/ x (+ x y))
42.0ms	(* x (log (/ x (+ x y))))
12.0ms	(log (/ x (+ x y)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ x (+ x y))
96.0ms	(* x (log (/ x (+ x y))))
65.0ms	(log (/ x (+ x y)))

simplify2.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5030
3	3902
2	806
1	357
0	170

prune614.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

144×	`log-prod`
138×	`cbrt-prod`
126×	`times-frac`
122×	`*-un-lft-identity`
86×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`distribute-lft-out`
13×	`add-exp-log`
7×	`pow1`
6×	`cbrt-div` `rem-log-exp` `associate-/r/`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `div-inv`
1×	`pow1/3`

Counts

4 → 192

Calls

4 calls:

1.0ms	(cbrt x)
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
11.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt x)
110.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
100.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
135.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify2.2s

Counts

204 → 204

Iterations

Iter	Nodes
done	5004
4	3730
3	1468
2	549
1	320
0	175

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt x) (cbrt x)))
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
15.8b	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

109×	`log-prod`
95×	`cbrt-prod`
91×	`times-frac`
87×	`*-un-lft-identity`
61×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-exp-log`
13×	`distribute-lft-out`
7×	`pow1` `rem-log-exp`
6×	`cbrt-div` `associate-/r/`
4×	`add-cbrt-cube` `div-exp` `insert-posit16` `add-log-exp`
3×	`log-div` `flip3-+` `log-pow` `flip-+` `div-inv`
1×	`pow1/3` `prod-exp`

Counts

4 → 156

Calls

4 calls:

5.0ms	(cbrt (* (cbrt x) (cbrt x)))
13.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
14.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
18.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(cbrt (* (cbrt x) (cbrt x)))
124.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
113.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
81.0ms	(log (/ (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (cbrt x))) (cbrt (+ x y))))

simplify2.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
4	3573
3	1583
2	635
1	373
0	207

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize144.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
2.2b	(log (/ (cbrt x) (cbrt (+ x y))))
2.3b	(log (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))))
21.9b	(log (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

280×	`cbrt-prod`
208×	`log-prod`
178×	`times-frac`
160×	`*-un-lft-identity`
118×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`cbrt-div`
21×	`distribute-lft-out`
19×	`add-exp-log`
14×	`associate-/r/`
9×	`flip3-+` `rem-log-exp` `flip-+`
8×	`pow1`
5×	`div-exp`
4×	`frac-times` `log-div` `add-cbrt-cube` `log-pow` `insert-posit16` `div-inv` `add-log-exp`
2×	`associate-l/` `associate-r/`
1×	`prod-exp`

Counts

4 → 257

Calls

4 calls:

11.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
8.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
16.0ms	(log (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))))
37.0ms	(log (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
110.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
103.0ms	(log (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))))
127.0ms	(log (/ (cbrt (* (cbrt x) (cbrt x))) (* (cbrt (cbrt (+ x y))) (cbrt (cbrt (+ x y))))))

simplify2.2s

Counts

269 → 269

Iterations

Iter	Nodes
done	5004
3	3358
2	1193
1	791
0	455

prune2.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

regimes139.0ms

Accuracy

56.5% (1.7b remaining)

Error of 3.2b against oracle of 1.5b and baseline of 5.5b

bsearch117.0ms

Steps

Iters	Range		Point
8	73049.03827748532	84262549.71201208	74347.0824335901

simplify19.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.5s	1539×	body	1280	valid
641.0ms	1467×	body	640	valid
558.0ms	4850×	body	80	valid
260.0ms	826×	body	320	valid
207.0ms	2996×	body	80	nan
73.0ms	436×	body	160	valid