Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	60×	body	1280	valid
3.0ms	32×	body	640	valid
3.0ms	124×	body	80	valid
2.0ms	33×	body	320	valid
1.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
23.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series442.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(cbrt (+ x 1.0))
184.0ms	(cbrt x)
159.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify882.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (263.0ms)

Iter	Nodes	Cost
0	131	649
1	291	597
2	698	573
3	1810	521
done	5001	521

prune142.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

57×	`cbrt-prod`
33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
12×	`difference-of-squares`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `distribute-lft-out--`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube` `distribute-lft-out`
3×	`pow1/3`
2×	`cube-div` `flip3--` `flip--`
1×	`cube-mult` `sub-neg` `flip3-+` `diff-log` `unpow3` `rem-cbrt-cube` `flip-+` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

25.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
26.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series603.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
94.0ms	(cbrt (+ x 1.0))
188.0ms	(cbrt x)
160.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: 3 (482.0ms)

Iter	Nodes	Cost
0	181	1499
1	428	1213
2	1143	1163
3	3742	1082
done	5001	1082

prune238.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
12.7b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

20.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
3.0ms	(cbrt (cbrt (+ x 1.0)))
0.0ms	(cbrt x)
21.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series568.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
99.0ms	(cbrt (cbrt (+ x 1.0)))
188.0ms	(cbrt x)
162.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.8s

Counts

105 → 105

Iterations

Useful iterations: 3 (784.0ms)

Iter	Nodes	Cost
0	233	1653
1	518	1521
2	1355	1407
3	4377	1261
done	5000	1261

prune300.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.5b	(pow (cbrt (cbrt (+ x 1.0))) 4)
0.6b	(cbrt x)
19.3b	(- (* (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
15×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `add-cbrt-cube`
3×	`pow-unpow` `pow1/3`
2×	`pow-pow` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `flip3-+` `diff-log` `pow-exp` `flip--` `flip-+` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
6.0ms	(pow (cbrt (cbrt (+ x 1.0))) 4)
0.0ms	(cbrt x)
42.0ms	(- (* (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series591.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (cbrt (+ x 1.0)))
158.0ms	(pow (cbrt (cbrt (+ x 1.0))) 4)
182.0ms	(cbrt x)
157.0ms	(- (* (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) 4))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.6s

Counts

77 → 77

Iterations

Useful iterations: 3 (680.0ms)

Iter	Nodes	Cost
0	238	1412
1	555	1325
2	1494	1221
3	4672	1095
done	5000	1095

prune269.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.8b

regimes100.0ms

Accuracy

98.2% (0.4b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 29.9b

bsearch63.0ms

Steps

Iters	Range		Point
6	0.0591185632533196	0.44834868164545755	0.10532502913683747
8	-133622.27441454158	-436.72743869654124	-3435.2945499089387

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	48	70
1	58	68
done	58	68

end0.0ms

sample503.0ms

Algorithm

intervals

Results

170.0ms	1680×	body	1280	valid
95.0ms	1245×	body	640	valid
93.0ms	4078×	body	80	valid
37.0ms	660×	body	320	valid
13.0ms	337×	body	160	valid