Details

sample100.0ms

Algorithm

intervals

Results

43.0ms	59×	body	1280	valid
14.0ms	51×	body	640	valid
12.0ms	309×	body	80	nan
8.0ms	117×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	6×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize17.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

12.0ms	(- (log (+ N 1.0)) (log N))
10.0ms	(log (+ N 1.0))

series174.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(- (log (+ N 1.0)) (log N))
54.0ms	(log (+ N 1.0))

simplify3.7s

Counts

47 → 47

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	101	510
1	416	481
done	5001	445

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.3333333333333333 (pow N 3))
0.3b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.8b	(/ 0.5 (* N N))
10.8b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
31×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 124

Calls

4 calls:

17.0ms	(/ 0.3333333333333333 (pow N 3))
49.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
15.0ms	(/ 0.5 (* N N))
169.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 0.3333333333333333 (pow N 3))
125.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
43.0ms	(/ 0.5 (* N N))
53.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	209	1839
done	5000	1614

prune383.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 0.5 (* N N))
4.1b	(exp (log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))))
10.8b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))
17.5b	(log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N)))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
10×	`add-exp-log` `log-div` `log-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `distribute-lft-out`
5×	`exp-diff` `exp-sum`
4×	`exp-prod`
3×	`flip3--` `flip3-+` `times-frac` `frac-sub` `flip--` `flip-+` `associate-/l*` `distribute-lft-out--`
2×	`cbrt-undiv` `associate-+r+` `div-exp` `sum-log` `log-pow`
1×	`+-commutative` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

8.0ms	(/ 0.5 (* N N))
109.0ms	(exp (log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))))
130.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))
125.0ms	(log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N)))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 0.5 (* N N))
56.0ms	(exp (log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))))
56.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))
148.0ms	(log (+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N)))))

simplify2.5s

Counts

94 → 94

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	194	2215
1	1407	1980
done	5001	1802

prune367.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 0.125 (* (pow N 2) (pow 1.0 2)))
0.8b	(/ 0.3333333333333333 (* N N))
3.2b	(exp (- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2))))))
10.9b	(- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2)))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
40×	`distribute-lft-out--`
39×	`add-log-exp`
32×	`add-exp-log` `distribute-lft-out`
20×	`pow1`
16×	`exp-prod` `diff-log` `log-pow`
14×	`sum-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
12×	`div-exp` `frac-sub`
10×	`frac-add` `prod-exp`
9×	`add-cube-cbrt`
7×	`flip3-+` `flip-+` `rem-exp-log`
6×	`pow-to-exp` `times-frac` `pow-exp` `associate-/l*`
4×	`cbrt-undiv` `flip3--` `flip--`
3×	`exp-sum`
2×	`sub-neg` `frac-2neg` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`associate--l-` `associate-+r-` `exp-diff` `associate--r+`

Counts

4 → 129

Calls

4 calls:

17.0ms	(/ 0.125 (* (pow N 2) (pow 1.0 2)))
15.0ms	(/ 0.3333333333333333 (* N N))
1.2s	(exp (- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2))))))
513.0ms	(- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2)))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ 0.125 (* (pow N 2) (pow 1.0 2)))
35.0ms	(/ 0.3333333333333333 (* N N))
121.0ms	(exp (- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2))))))
84.0ms	(- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2)))))

simplify2.3s

Counts

141 → 141

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	285	3819
1	2802	3567
done	5001	3356

prune546.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch46.0ms

Steps

Iters	Range		Point
9	0.00565890190154967	18133.886566758163	3775.8969182145884

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	28
1	23	28
done	23	28

end0.0ms

sample3.1s

Algorithm

intervals

Results

898.0ms	8101×	body	80	nan
847.0ms	1746×	body	1280	valid
397.0ms	1216×	body	640	valid
298.0ms	4125×	body	80	valid
149.0ms	614×	body	320	valid
34.0ms	299×	body	160	valid