Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	54×	body	1280	valid
3.0ms	39×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 30.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite44.0ms

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:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
39.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series415.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
152.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.9s

Counts

53 → 53

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	131	649
1	290	597
2	672	573
3	1717	521
4	4878	501
done	5000	501

prune141.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
23.0b	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 51

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
80.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series493.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ x 1.0))
86.0ms	(cbrt (+ x 1.0))
174.0ms	(cbrt x)
147.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.1s

Counts

63 → 63

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	126	1011
1	291	963
2	699	686
3	1877	592
done	5000	565

prune180.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

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)
3.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite89.0ms

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:

40.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
41.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (pow (- (cbrt (+ x 1.0)) (cbrt x)) 3))
89.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	181	1499
1	426	1213
2	1119	1163
3	4107	1082
done	5000	1054

prune223.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ 0.3333333333333333 (* 0.05555555555555555 x)))
0.4b	(* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6)
0.6b	(cbrt x)
15.9b	(- (* (cbrt 1.0) (+ (* x (+ 0.3333333333333333 (* 0.05555555555555555 x))) 1)) (* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
13×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-*r/` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r` `add-log-exp`
4×	`associate-l`
3×	`cbrt-prod` `cbrt-div` `associate-*l/`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate--l+` `*-commutative` `frac-sub` `flip-+`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

15.0ms	(* x (+ 0.3333333333333333 (* 0.05555555555555555 x)))
72.0ms	(* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6)
1.0ms	(cbrt x)
38.0ms	(- (* (cbrt 1.0) (+ (* x (+ 0.3333333333333333 (* 0.05555555555555555 x))) 1)) (* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6))

series695.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* x (+ 0.3333333333333333 (* 0.05555555555555555 x)))
299.0ms	(* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6)
182.0ms	(cbrt x)
150.0ms	(- (* (cbrt 1.0) (+ (* x (+ 0.3333333333333333 (* 0.05555555555555555 x))) 1)) (* (* (* x x) (cbrt (/ 1 (pow 1.0 5)))) 1/6))

simplify1.1s

Counts

83 → 83

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	176	1464
1	484	1344
2	1898	1211
done	5001	1195

prune246.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes79.0ms

Accuracy

96.1% (1.2b remaining)

Error of 1.4b against oracle of 0.3b and baseline of 29.6b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	58
1	53	58
done	53	58

end0.0ms

sample516.0ms

Algorithm

intervals

Results

164.0ms	1680×	body	1280	valid
96.0ms	1236×	body	640	valid
84.0ms	4124×	body	80	valid
38.0ms	644×	body	320	valid
12.0ms	316×	body	160	valid