Details

sample75.0ms

Algorithm

intervals

Results

23.0ms	60×	body	1280	valid
11.0ms	37×	body	640	valid
11.0ms	243×	body	80	nan
9.0ms	131×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	8×	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: 29.5b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
2.1b	(- (log (+ N 1.0)) (log N))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

5.0ms	(log (+ N 1.0))
14.0ms	(- (log (+ N 1.0)) (log N))

series205.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(log (+ N 1.0))
152.0ms	(- (log (+ N 1.0)) (log N))

simplify3.1s

Counts

47 → 47

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	464	445
3	1067	443
4	2569	438
done	5000	426

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (log (+ N 1.0)) 3))
0.4b	(pow (log (+ N 1.0)) 3)
2.0b	(log (+ N 1.0))
2.1b	(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`cbrt-prod`
17×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`pow1`
9×	`unpow-prod-down` `cube-prod`
7×	`log-prod`
6×	`add-exp-log` `log-pow`
5×	`add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `associate--r+` `sqr-pow`
2×	`cube-mult` `log-div` `unpow3` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

6.0ms	(cbrt (pow (log (+ N 1.0)) 3))
9.0ms	(pow (log (+ N 1.0)) 3)
9.0ms	(log (+ N 1.0))
46.0ms	(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))

series416.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (pow (log (+ N 1.0)) 3))
145.0ms	(pow (log (+ N 1.0)) 3)
68.0ms	(log (+ N 1.0))
143.0ms	(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))

simplify1.1s

Counts

97 → 97

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	203	1422
1	488	1149
2	1358	1046
done	5001	1030

prune290.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
2.0b	(log (+ N 1.0))
23.1b	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `associate--l+`
9×	`cbrt-prod`
6×	`pow1` `associate--r+` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`diff-log`
2×	`sub-neg` `log-div` `pow1/3` `log-pow` `distribute-lft-out` `distribute-lft-out--`
1×	`associate--l-` `flip3--` `flip3-+` `rem-log-exp` `flip--` `flip-+` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(log (+ N 1.0))
68.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt N)
276.0ms	(cbrt N)
51.0ms	(log (+ N 1.0))
115.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

simplify2.4s

Counts

78 → 78

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	141	922
1	326	820
2	815	698
3	2712	622
done	5000	600

prune260.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
0.1b	(/ 0.3333333333333333 (pow N 3))
0.2b	(/ 0.5 (* N N))
14.2b	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite682.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity` `times-frac`
35×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `sqr-pow`
3×	`cbrt-undiv` `frac-sub` `distribute-lft-out`
2×	`frac-2neg` `flip3-+` `diff-log` `frac-add` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `prod-exp` `associate--l+` `flip--` `cbrt-unprod`

Counts

4 → 121

Calls

4 calls:

54.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
9.0ms	(/ 0.3333333333333333 (pow N 3))
8.0ms	(/ 0.5 (* N N))
606.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
66.0ms	(/ 0.3333333333333333 (pow N 3))
36.0ms	(/ 0.5 (* N N))
51.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify1.1s

Counts

133 → 133

Iterations

Useful iterations: 2 (371.0ms)

Iter	Nodes	Cost
0	201	1812
1	444	1577
2	1579	1491
done	5000	1491

prune368.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch35.0ms

Steps

Iters	Range		Point
5	3739.899882177282	9207.496297094358	4795.8485539057265

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	22	27
done	22	27

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	1720×	body	1280	valid
475.0ms	7865×	body	80	nan
415.0ms	1262×	body	640	valid
361.0ms	4152×	body	80	valid
105.0ms	592×	body	320	valid
31.0ms	274×	body	160	valid