Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	63×	body	1280	valid
9.0ms	282×	body	80	nan
9.0ms	49×	body	640	valid
6.0ms	116×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
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 (+ 1.0 N))
15.0ms	(- (log (+ 1.0 N)) (log N))

series169.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(log (+ 1.0 N))
118.0ms	(- (log (+ 1.0 N)) (log N))

simplify966.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1094
1	287
0	126

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

8564×	`times-frac`
4846×	`add-sqr-sqrt`
4809×	`*-un-lft-identity`
4792×	`add-cube-cbrt`
3440×	`prod-diff`
1722×	`associate-+r+`
798×	`unpow-prod-down` `cube-prod`
414×	`div-inv`
268×	`sqr-pow`
265×	`cube-mult` `unpow3`
40×	`fma-neg`
16×	`associate-/l*`
15×	`associate-/r*` `difference-of-squares`
14×	`add-exp-log`
13×	`fma-def`
11×	`add-cbrt-cube` `add-log-exp`
6×	`div-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `log1p-expm1-u` `distribute-lft-out--`
3×	`frac-add` `distribute-lft-out`
2×	`clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

4 → 3687

Calls

4 calls:

472.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)))
10.0ms	(/ (/ 0.5 N) N)
8.0ms	(/ 0.3333333333333333 (pow N 3))
167.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

series232.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N)))
31.0ms	(/ (/ 0.5 N) N)
62.0ms	(/ 0.3333333333333333 (pow N 3))
106.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))

simplify2.6s

Counts

3699 → 3699

Iterations

Iter	Nodes
done	5000
0	3157

prune17.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

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

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

1016×	`*-un-lft-identity`
860×	`times-frac`
482×	`add-sqr-sqrt`
444×	`add-cube-cbrt`
430×	`prod-diff`
184×	`distribute-lft-out`
40×	`div-inv`
18×	`sqrt-prod`
14×	`add-log-exp`
12×	`frac-sub` `distribute-lft-out--` `difference-of-squares`
10×	`fma-neg` `sqrt-div`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip3--` `add-cbrt-cube` `diff-log` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `associate--l+`

Counts

4 → 542

Calls

4 calls:

546.0ms	(sqrt (- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N)))
572.0ms	(sqrt (- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N)))
980.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N))
691.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N))

series253.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N)))
77.0ms	(sqrt (- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N)))
38.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N))
38.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ (/ 0.5 N) N))

simplify874.0ms

Counts

554 → 554

Iterations

Iter	Nodes
done	5000
1	1483
0	568

prune2.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

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

series185.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(/ (+ 1.0 N) N)
128.0ms	(log (/ (+ 1.0 N) N))

simplify665.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1036
1	252
0	111

prune297.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch41.0ms

Steps

Iters	Range		Point
8	2205.5689030668646	18639768.73979092	4798.860931730866

simplify2.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample2.5s

Algorithm

intervals

Results

788.0ms	1710×	body	1280	valid
465.0ms	8079×	body	80	nan
398.0ms	1245×	body	640	valid
284.0ms	4111×	body	80	valid
159.0ms	659×	body	320	valid
29.0ms	275×	body	160	valid