Details

sample105.0ms

Algorithm

intervals

Results

26.0ms	49×	body	1280	valid
16.0ms	17×	body	320	valid
13.0ms	250×	body	80	nan
13.0ms	142×	body	80	valid
12.0ms	36×	body	640	valid
2.0ms	12×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize17.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (+ N 1.0))
3.1b	(- (log (+ N 1.0)) (log N))

rewrite31.0ms

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))
25.0ms	(- (log (+ N 1.0)) (log N))

series169.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
123.0ms	(- (log (+ N 1.0)) (log N))

simplify1.5s

Counts

47 → 47

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	644	445
3	2755	443
done	5001	438

prune206.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.2b	(log (/ (+ N 1.0) N))

rewrite37.0ms

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:

26.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series184.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (+ N 1.0) N)
114.0ms	(log (/ (+ N 1.0) N))

simplify703.0ms

Counts

66 → 66

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	108	723
1	243	690
2	1010	637
done	5000	624

prune170.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.3b	(/ 0.3333333333333333 (pow N 3))
0.3b	(/ 0.5 (* N N))
13.6b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
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` `difference-of-squares` `sqr-pow`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `associate-+l+` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+l-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 124

Calls

4 calls:

39.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
18.0ms	(/ 0.3333333333333333 (pow N 3))
17.0ms	(/ 0.5 (* N N))
198.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
69.0ms	(/ 0.3333333333333333 (pow N 3))
30.0ms	(/ 0.5 (* N N))
41.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ 0.3333333333333333 (pow N 3)))

simplify3.3s

Counts

136 → 136

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	210	1847
1	534	1627
2	3960	1528
done	5000	1528

prune436.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (/ 0.3333333333333333 (pow N 3)))
16.7b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
16.7b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
16.7b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

153×	`cbrt-div`
81×	`frac-times`
63×	`frac-add`
51×	`flip3--` `frac-sub` `flip--`
37×	`add-sqr-sqrt`
27×	`associate-*l/`
24×	`cbrt-prod`
15×	`associate-*r/`
13×	`*-un-lft-identity`
12×	`times-frac` `difference-of-squares`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `distribute-lft-out--`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 131

Calls

4 calls:

308.0ms	(+ (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (/ 0.3333333333333333 (pow N 3)))
18.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
30.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
24.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(+ (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (/ 0.3333333333333333 (pow N 3)))
156.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
199.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
199.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify2.5s

Counts

143 → 143

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	475	10453
1	1167	9636
2	3794	8470
done	5001	8413

prune636.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.2b

bsearch43.0ms

Steps

Iters	Range		Point
9	0.02325869037085268	28918.939680702064	9187.863337025456

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

777.0ms	4095×	body	80	valid
727.0ms	1784×	body	1280	valid
495.0ms	7835×	body	80	nan
356.0ms	1229×	body	640	valid
153.0ms	618×	body	320	valid
30.0ms	274×	body	160	valid