Details

sample102.0ms

Algorithm

intervals

Results

34.0ms	63×	body	1280	valid
17.0ms	49×	body	640	valid
15.0ms	282×	body	80	nan
10.0ms	116×	body	80	valid
4.0ms	17×	body	320	valid
2.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize32.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ 1.0 N))
2.9b	(- (log (+ 1.0 N)) (log N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
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:

4.0ms	(log (+ 1.0 N))
11.0ms	(- (log (+ 1.0 N)) (log N))

series182.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(log (+ 1.0 N))
135.0ms	(- (log (+ 1.0 N)) (log N))

simplify1.3s

Counts

47 → 47

Iterations

Iter	Nodes
done	5001
3	2644
2	631
1	213
0	100

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)) (/ 1.0 N))
0.1b	(/ (/ 0.5 N) N)
0.3b	(/ 0.3333333333333333 (pow N 3))
10.8b	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

rewrite915.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
125×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
71×	`add-cube-cbrt`
16×	`associate-/l*`
15×	`associate-/r*` `unpow-prod-down` `cube-prod` `difference-of-squares`
14×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
7×	`sqr-pow`
6×	`div-exp` `div-inv`
4×	`cube-mult` `pow1` `cbrt-undiv` `unpow3` `distribute-lft-out--`
3×	`frac-add` `distribute-lft-out`
2×	`associate-+l+` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`pow-to-exp` `+-commutative` `flip3-+` `pow-exp` `associate-+l-` `flip-+` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

765.0ms	(+ (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)) (/ 1.0 N))
16.0ms	(/ (/ 0.5 N) N)
9.0ms	(/ 0.3333333333333333 (pow N 3))
118.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

series315.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)) (/ 1.0 N))
36.0ms	(/ (/ 0.5 N) N)
75.0ms	(/ 0.3333333333333333 (pow N 3))
169.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

simplify2.8s

Counts

198 → 198

Iterations

Iter	Nodes
done	5001
2	4212
1	786
0	317

prune769.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

8.7b	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
8.7b	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
10.8b	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
10.8b	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite740.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
30×	`times-frac`
24×	`*-un-lft-identity`
20×	`difference-of-squares`
10×	`sqrt-div` `sqrt-prod`
8×	`add-log-exp`
6×	`pow1` `frac-add` `add-cube-cbrt` `distribute-lft-out--`
4×	`unpow-prod-down` `flip3--` `add-cbrt-cube` `cube-prod` `add-exp-log` `frac-sub` `flip--` `distribute-lft-out` `sqr-pow`
2×	`cube-mult` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 90

Calls

4 calls:

272.0ms	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
309.0ms	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
91.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
62.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
75.0ms	(sqrt (+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))))
144.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))
136.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify900.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1387
1	343
0	138

prune670.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 N) N)
3.3b	(log (/ (+ 1.0 N) N))

rewrite21.0ms

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` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

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

series203.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (+ 1.0 N) N)
131.0ms	(log (/ (+ 1.0 N) N))

simplify550.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
2	1011
1	243
0	107

prune230.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch31.0ms

Steps

Iters	Range		Point
8	2205.5689030668646	18639768.73979092	4798.860931730866

simplify2.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample2.9s

Algorithm

intervals

Results

815.0ms	1710×	body	1280	valid
776.0ms	8079×	body	80	nan
357.0ms	4111×	body	80	valid
314.0ms	1245×	body	640	valid
177.0ms	659×	body	320	valid
28.0ms	275×	body	160	valid