Details

sample45.0ms

Algorithm

intervals

Results

13.0ms	51×	body	1280	valid
6.0ms	284×	body	80	nan
6.0ms	141×	body	80	valid
5.0ms	33×	body	640	valid
2.0ms	23×	body	320	valid
0.0ms	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: 27.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (log (+ N 1.0)) (log N))
3.4b	(log (+ N 1.0))

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:

15.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series144.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(- (log (+ N 1.0)) (log N))
45.0ms	(log (+ N 1.0))

simplify1.9s

Counts

47 → 47

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	462	445
3	1063	443
4	2574	438
done	5001	426

prune100.0ms

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)
2.8b	(log (/ (+ N 1.0) N))

rewrite25.0ms

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:

17.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series141.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (+ N 1.0) N)
87.0ms	(log (/ (+ N 1.0) N))

simplify2.4s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	108	723
1	232	690
2	583	637
3	1417	624
4	3874	622
done	5001	622

prune114.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
3.2b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
55×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
37×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
8×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 107

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
54.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt N)
182.0ms	(cbrt N)
178.0ms	(cbrt N)
250.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify1.5s

Counts

119 → 119

Iterations

Useful iterations: 3 (656.0ms)

Iter	Nodes	Cost
0	229	2047
1	509	1900
2	1291	1631
3	4398	1495
done	5000	1495

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
3.4b	(log (sqrt (sqrt (+ N 1.0))))
6.0b	(pow N 2/3)
27.2b	(+ (log (/ (sqrt (sqrt (+ N 1.0))) (cbrt N))) (+ (log (sqrt (sqrt (+ N 1.0)))) (log (/ (sqrt (+ N 1.0)) (pow N 2/3)))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
77×	`sqrt-prod`
74×	`log-prod`
64×	`associate-+l+`
60×	`times-frac`
49×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`cbrt-prod`
25×	`distribute-lft-out`
21×	`pow1`
18×	`log-pow`
8×	`sqrt-div`
6×	`add-exp-log` `log-div`
5×	`add-log-exp`
4×	`associate-+r-` `sqrt-pow1` `add-cbrt-cube`
3×	`associate-+l-` `unpow-prod-down` `pow-unpow` `flip3-+` `sum-log` `flip-+`
2×	`pow1/2`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

1.0ms	(cbrt N)
6.0ms	(log (sqrt (sqrt (+ N 1.0))))
2.0ms	(pow N 2/3)
62.0ms	(+ (log (/ (sqrt (sqrt (+ N 1.0))) (cbrt N))) (+ (log (sqrt (sqrt (+ N 1.0)))) (log (/ (sqrt (+ N 1.0)) (pow N 2/3)))))

series952.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt N)
128.0ms	(log (sqrt (sqrt (+ N 1.0))))
189.0ms	(pow N 2/3)
446.0ms	(+ (log (/ (sqrt (sqrt (+ N 1.0))) (cbrt N))) (+ (log (sqrt (sqrt (+ N 1.0)))) (log (/ (sqrt (+ N 1.0)) (pow N 2/3)))))

simplify754.0ms

Counts

156 → 156

Iterations

Useful iterations: done (749.0ms)

Iter	Nodes	Cost
0	310	3338
1	737	3263
2	2019	3138
done	5001	2907

prune580.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes19.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.7b

bsearch32.0ms

Steps

Iters	Range		Point
8	211.08706756948936	1126179.5725289274	12267.95132095184

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.3s

Algorithm

intervals

Results

433.0ms	1727×	body	1280	valid
195.0ms	1204×	body	640	valid
182.0ms	8130×	body	80	nan
173.0ms	4160×	body	80	valid
62.0ms	618×	body	320	valid
18.0ms	291×	body	160	valid