Details

sample84.0ms

Algorithm

intervals

Results

14.0ms	186×	body	80	valid
14.0ms	19×	body	640	valid
11.0ms	29×	body	1280	valid
7.0ms	119×	body	80	nan
6.0ms	19×	body	1280	nan
3.0ms	14×	body	640	nan
2.0ms	12×	body	160	valid
2.0ms	10×	body	320	valid
1.0ms	8×	body	320	nan
0.0ms	2×	body	160	nan

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	29	12
3	41	12
4	75	12
5	124	12
6	208	12
7	320	12
8	772	12
9	3045	12
done	5001	12

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.9b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
27×	`times-frac`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`distribute-lft-out--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`log-div` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `div-inv` `associate--r-`

Counts

3 → 85

Calls

3 calls:

37.0ms	(/ (- x y) (- 1.0 y))
52.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
37.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series234.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- x y) (- 1.0 y))
59.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
125.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify782.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (253.0ms)

Iter	Nodes	Cost
0	171	1417
1	407	1351
2	1389	1266
done	5001	1266

prune344.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
3.9b	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
11.6b	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `flip--`
8×	`associate-r` `associate-l`
7×	`add-exp-log` `pow1/3` `distribute-lft-out--`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`log-prod`
2×	`log-div` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

7.0ms	(cbrt (- 1.0 y))
64.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
4.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
6.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (- 1.0 y))
128.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
101.0ms	(log (- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y))))))
87.0ms	(- 1.0 (* (/ 1 (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (/ (- x y) (cbrt (- 1.0 y)))))

simplify871.0ms

Counts

109 → 109

Iterations

Useful iterations: done (865.0ms)

Iter	Nodes	Cost
0	212	2226
1	500	2066
2	1855	1819
done	5001	1793

prune392.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))
3.5b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
3.5b	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
18×	`log-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
8×	`pow1` `add-cube-cbrt` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3--` `times-frac` `sqrt-div` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `rem-log-exp` `associate--r-`

Counts

4 → 76

Calls

4 calls:

40.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
61.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
66.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
55.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
69.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
143.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))
157.0ms	(log (sqrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (415.0ms)

Iter	Nodes	Cost
0	114	1602
1	229	1526
2	654	1394
3	2745	1386
done	5000	1386

prune302.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
3.0b	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
11.2b	(log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))
12.8b	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
73×	`difference-of-squares`
72×	`log-prod`
54×	`unpow-prod-down` `cube-prod`
42×	`*-un-lft-identity`
33×	`associate--l+`
30×	`sqr-pow`
24×	`times-frac`
19×	`distribute-lft-out--`
10×	`pow1`
8×	`add-cube-cbrt` `log-div`
6×	`add-exp-log` `log-pow` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `flip--`
3×	`difference-cubes` `associate--r+`
2×	`associate--l-` `sub-neg` `flip3-+` `diff-log` `rem-log-exp` `flip-+` `associate--r-`

Counts

4 → 157

Calls

4 calls:

164.0ms	(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
104.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
61.0ms	(log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))
168.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

series1.5s

Counts

4 → 12

Calls

4 calls:

601.0ms	(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
290.0ms	(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
220.0ms	(log (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))
435.0ms	(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

simplify1.2s

Counts

169 → 169

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	263	5772
1	615	5449
2	2193	5258
done	5002	5254

prune724.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes183.0ms

Accuracy

95.6% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 16.6b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	53
1	33	53
done	33	53

end0.0ms

sample2.5s

Algorithm

intervals

Results

987.0ms	5721×	body	80	valid
290.0ms	780×	body	1280	valid
191.0ms	801×	body	640	valid
181.0ms	3901×	body	80	nan
148.0ms	447×	body	320	valid
102.0ms	377×	body	1280	nan
79.0ms	389×	body	640	nan
34.0ms	195×	body	320	nan
27.0ms	251×	body	160	valid
11.0ms	119×	body	160	nan