Details

sample46.0ms

Algorithm

intervals

Results

14.0ms	57×	body	1280	valid
8.0ms	53×	body	640	valid
6.0ms	267×	body	80	nan
5.0ms	118×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	8×	body	160	valid

simplify5.0ms

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: 32.1b

localize10.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
2.5b	(- (log (+ N 1.0)) (log N))

rewrite20.0ms

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:

4.0ms	(log (+ N 1.0))
14.0ms	(- (log (+ N 1.0)) (log N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify130.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343
done	5001	343

prune128.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.9b	(/ 1 (pow N 2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*`
6×	`div-exp`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 69

Calls

2 calls:

0.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
8.0ms	(/ 1 (pow N 2))

series53.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
17.0ms	(/ 1 (pow N 2))

simplify30.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	208	384
1	789	315
2	5001	269
done	5001	269

prune99.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.4b	(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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

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

series136.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344
done	5001	344

prune117.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ N 1.0))
0.1b	(/ (sqrt (+ N 1.0)) N)
0.2b	(* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N))
17.4b	(log (* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
41×	`sqrt-prod`
37×	`add-cube-cbrt`
25×	`associate-r`
17×	`add-exp-log`
12×	`sqrt-div`
11×	`add-cbrt-cube`
10×	`pow1`
9×	`distribute-lft-out`
7×	`associate-l` `associate-/l*`
6×	`flip3-+` `flip-+` `unswap-sqr`
5×	`log-div`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `rem-log-exp` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `pow-prod-down` `log-pow` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`rem-sqrt-square` `log-prod` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `hypot-def`

Counts

4 → 144

Calls

4 calls:

8.0ms	(sqrt (+ N 1.0))
15.0ms	(/ (sqrt (+ N 1.0)) N)
47.0ms	(* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N))
18.0ms	(log (* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ N 1.0))
73.0ms	(/ (sqrt (+ N 1.0)) N)
47.0ms	(* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N))
87.0ms	(log (* (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N)))

simplify52.0ms

Counts

156 → 156

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	448	1124
1	1790	1000
2	5002	931
done	5002	931

prune297.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes25.0ms

Accuracy

100% (0.0b remaining)

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

bsearch22.0ms

Steps

Iters	Range		Point
7	6136.975143603057	736927.0597324986	9607.783785361795

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9
done	21	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

427.0ms	1803×	body	1280	valid
185.0ms	1234×	body	640	valid
178.0ms	8113×	body	80	nan
165.0ms	4021×	body	80	valid
66.0ms	634×	body	320	valid
18.0ms	308×	body	160	valid