Details

sample49.0ms

Algorithm

intervals

Results

18.0ms	66×	body	1280	valid
6.0ms	46×	body	640	valid
6.0ms	278×	body	80	nan
5.0ms	114×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize7.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (log (+ N 1.0)) (log N))
2.5b	(log (+ N 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

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

series131.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log (+ N 1.0)) (log N))
43.0ms	(log (+ N 1.0))

simplify118.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (113.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345
done	5001	345

prune133.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.5b	(/ 1 (pow N 2))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
172×	`add-cube-cbrt`
165×	`times-frac`
156×	`prod-diff`
82×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
14×	`div-inv`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 313

Calls

3 calls:

45.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
82.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
9.0ms	(/ 1 (pow N 2))

series121.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
74.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms	(/ 1 (pow N 2))

simplify115.0ms

Counts

322 → 322

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1021	3505
1	4524	2419
2	5001	2419
done	5001	2419

prune665.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

2.5b	(log (/ (+ N 1.0) N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`expm1-log1p-u` `log-div` `div-exp` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

6.0ms

(log (/ (+ N 1.0) N))

series81.0ms

Counts

1 → 3

Calls

1 calls:

81.0ms

(log (/ (+ N 1.0) N))

simplify57.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	172	216
1	471	200
2	2042	190
3	5002	187
done	5002	187

prune62.0ms

Pruning

5 alts after pruning (3 fresh and 2 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)
3.1b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
56×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
9×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
62.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series758.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt N)
179.0ms	(cbrt N)
173.0ms	(cbrt N)
233.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify49.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	515	1353
1	1641	1284
2	5001	1181
done	5001	1181

prune371.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch18.0ms

Steps

Iters	Range		Point
6	5364.146891578128	78679.13042368767	9757.882283737008

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10
done	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

400.0ms	1721×	body	1280	valid
194.0ms	1332×	body	640	valid
171.0ms	8018×	body	80	nan
161.0ms	4039×	body	80	valid
56.0ms	606×	body	320	valid
19.0ms	302×	body	160	valid