Details

sample92.0ms

Algorithm

intervals

Results

33.0ms	63×	body	1280	valid
13.0ms	42×	body	640	valid
10.0ms	121×	body	80	valid
10.0ms	198×	body	80	nan
4.0ms	20×	body	320	valid
1.0ms	10×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(log (+ N 1.0))
2.6b	(- (log (+ N 1.0)) (log N))

rewrite26.0ms

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:

5.0ms	(log (+ N 1.0))
18.0ms	(- (log (+ N 1.0)) (log N))

series222.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(log (+ N 1.0))
164.0ms	(- (log (+ N 1.0)) (log N))

simplify3.6s

Counts

71 → 71

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	127	1052
1	277	855
2	666	705
3	2050	614
done	5000	592

prune174.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.0b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.3b	(/ 1 (pow N 2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt` `times-frac`
39×	`prod-diff`
13×	`fma-neg`
12×	`add-exp-log` `unpow-prod-down`
8×	`associate-/r*`
6×	`div-exp`
5×	`add-cbrt-cube` `div-inv` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`pow1` `expm1-log1p-u` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `clear-num` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow`

Counts

3 → 138

Calls

3 calls:

34.0ms	(- (/ 0.3333333333333333 N) 0.5)
1.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
11.0ms	(/ 1 (pow N 2))

series147.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (/ 0.3333333333333333 N) 0.5)
65.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
37.0ms	(/ 1 (pow N 2))

simplify2.6s

Counts

147 → 147

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	217	2158
1	423	1629
2	804	1336
3	2686	1168
done	5001	1128

prune285.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

20.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series215.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (+ N 1.0) N)
128.0ms	(log (/ (+ N 1.0) N))

simplify3.9s

Counts

70 → 70

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	112	749
1	242	708
2	620	660
3	1531	647
4	4287	643
done	5000	612

prune188.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
1.6b	(log (+ N 1.0))
23.0b	(- (fma -2 (log (cbrt N)) (log (+ N 1.0))) (log (cbrt N)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`prod-diff`
10×	`log-prod`
9×	`pow1` `cbrt-prod`
8×	`log-pow`
6×	`associate--r+`
5×	`add-exp-log` `pow1/3` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `rem-log-exp` `associate--l+` `flip--` `flip-+` `fma-udef` `distribute-lft-out` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(log (+ N 1.0))
12.0ms	(- (fma -2 (log (cbrt N)) (log (+ N 1.0))) (log (cbrt N)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(cbrt N)
315.0ms	(cbrt N)
77.0ms	(log (+ N 1.0))
209.0ms	(- (fma -2 (log (cbrt N)) (log (+ N 1.0))) (log (cbrt N)))

simplify4.0s

Counts

97 → 97

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	170	1547
1	368	1352
2	980	1120
3	3827	903
done	5000	898

prune410.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.9b

bsearch42.0ms

Steps

Iters	Range		Point
9	5.295671684036253	137362616.0762091	9454.187458193412

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	24
1	21	24
done	21	24

end0.0ms

sample2.6s

Algorithm

intervals

Results

824.0ms	1810×	body	1280	valid
495.0ms	8006×	body	80	nan
418.0ms	1244×	body	640	valid
323.0ms	3991×	body	80	valid
112.0ms	648×	body	320	valid
34.0ms	307×	body	160	valid