Details

sample43.0ms

Algorithm

intervals

Results

15.0ms	62×	body	1280	valid
6.0ms	40×	body	640	valid
5.0ms	122×	body	80	valid
5.0ms	226×	body	80	nan
2.0ms	22×	body	320	valid
1.0ms	10×	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: 31.3b

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (log (+ N 1.0)) (log N))
3.9b	(log (+ N 1.0))

rewrite10.0ms

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:

6.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series147.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (log (+ N 1.0)) (log N))
49.0ms	(log (+ N 1.0))

simplify782.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	101	510
1	213	488
2	513	445
3	1725	443
done	5001	443

prune103.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
0.4b	(/ 0.5 (* N N))
0.6b	(/ 0.3333333333333333 (pow N 3))
11.6b	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

100.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms	(/ 0.5 (* N N))
4.0ms	(/ 0.3333333333333333 (pow N 3))
41.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
24.0ms	(/ 0.5 (* N N))
41.0ms	(/ 0.3333333333333333 (pow N 3))
91.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify756.0ms

Counts

143 → 143

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	215	2088
1	507	1835
2	2123	1733
done	5001	1733

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

11.6b	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
18.0b	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
18.0b	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
18.0b	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
15×	`cbrt-prod` `cbrt-div` `times-frac`
10×	`difference-of-squares`
9×	`frac-add`
7×	`add-cube-cbrt`
6×	`distribute-lft-out` `add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`unpow-prod-down` `cube-prod` `sqr-pow`
1×	`cube-mult` `sub-neg` `diff-log`

Counts

4 → 79

Calls

4 calls:

40.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
88.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
87.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
91.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
160.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
156.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
158.0ms	(cbrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))

simplify473.0ms

Counts

91 → 91

Iterations

Useful iterations: done (468.0ms)

Iter	Nodes	Cost
0	175	2996
1	449	2866
2	1335	2726
done	5000	2685

prune325.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.0b	(log (/ (+ N 1.0) N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

8.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify1.2s

Counts

66 → 66

Iterations

Useful iterations: 3 (374.0ms)

Iter	Nodes	Cost
0	108	723
1	230	690
2	633	637
3	2886	624
done	5000	624

prune108.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.2b

bsearch30.0ms

Steps

Iters	Range		Point
9	0.08347146558812443	2231369.5462890854	9562.64518051556

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	20	25
done	20	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

435.0ms	1787×	body	1280	valid
187.0ms	1261×	body	640	valid
181.0ms	7984×	body	80	nan
166.0ms	4035×	body	80	valid
62.0ms	611×	body	320	valid
18.0ms	306×	body	160	valid