Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	62×	body	1280	valid
6.0ms	40×	body	640	valid
5.0ms	122×	body	80	valid
5.0ms	226×	body	80	nan
2.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize7.0ms

Local error

Found 2 expressions with local error:

3.1b	(- (log (+ N 1.0)) (log N))
3.9b	(log (+ N 1.0))

rewrite15.0ms

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:

7.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series131.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (log (+ N 1.0)) (log N))
41.0ms	(log (+ N 1.0))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (437.0ms)

Iter	Nodes	Cost
0	127	1052
1	273	855
2	710	705
3	2288	614
done	5000	614

prune128.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (/ 0.5 (* N N)))
0.4b	(/ 0.5 (* N N))
0.6b	(/ 0.3333333333333333 (pow N 3))
11.6b	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

292×	`times-frac`
220×	`add-sqr-sqrt`
217×	`*-un-lft-identity`
210×	`add-cube-cbrt`
182×	`prod-diff`
93×	`associate-+r+`
44×	`div-inv`
40×	`fma-def`
21×	`unpow-prod-down` `cube-prod`
14×	`add-exp-log`
13×	`fma-neg` `associate-/r*`
11×	`add-cbrt-cube` `add-log-exp`
7×	`cube-mult` `unpow3` `sqr-pow`
6×	`associate-/l*`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `frac-add`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `flip--` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+`

Counts

4 → 367

Calls

4 calls:

20.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
3.0ms	(/ 0.5 (* N N))
4.0ms	(/ 0.3333333333333333 (pow N 3))
81.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ 1.0 N) (/ 0.5 (* N N)))
27.0ms	(/ 0.5 (* N N))
35.0ms	(/ 0.3333333333333333 (pow N 3))
31.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify1.3s

Counts

379 → 379

Iterations

Useful iterations: 2 (631.0ms)

Iter	Nodes	Cost
0	444	8644
1	955	7099
2	2837	6141
done	5000	6141

prune795.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 0.5 (* N N))
0.6b	(/ 0.3333333333333333 (pow N 3))
11.6b	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))
14.3b	(fma (- (/ 0.5 (* N N))) 1 (* (/ 0.5 (* N N)) 1))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

4292×	`times-frac`
2453×	`add-sqr-sqrt`
2405×	`*-un-lft-identity`
2399×	`add-cube-cbrt`
1720×	`prod-diff`
411×	`unpow-prod-down` `cube-prod`
206×	`div-inv`
139×	`sqr-pow`
136×	`cube-mult` `unpow3`
40×	`fma-neg`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`associate-/r*`
11×	`add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv`
2×	`frac-2neg` `clear-num` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `fma-udef`

Counts

4 → 1892

Calls

4 calls:

4.0ms	(/ 0.5 (* N N))
6.0ms	(/ 0.3333333333333333 (pow N 3))
142.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))
0.0ms	(fma (- (/ 0.5 (* N N))) 1 (* (/ 0.5 (* N N)) 1))

series231.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 0.5 (* N N))
38.0ms	(/ 0.3333333333333333 (pow N 3))
88.0ms	(- (/ 0.3333333333333333 (pow N 3)) (/ (/ 0.5 N) N))
81.0ms	(fma (- (/ 0.5 (* N N))) 1 (* (/ 0.5 (* N N)) 1))

simplify1.6s

Counts

1904 → 1904

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	1792	115936
1	3285	102154
done	5000	99554

prune3.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

11.6b	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))
14.3b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
14.3b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
14.3b	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

153×	`cbrt-div`
81×	`frac-times`
63×	`frac-add`
59×	`add-sqr-sqrt`
51×	`flip3--` `frac-sub` `flip--`
48×	`times-frac`
40×	`fma-def`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`associate-*l/`
24×	`cbrt-prod`
15×	`associate-*r/`
12×	`difference-of-squares`
9×	`unpow-prod-down` `cube-prod`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cube-mult` `pow1/3` `unpow3` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 179

Calls

4 calls:

43.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))
11.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
10.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
14.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

series468.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (* (* (cbrt (- (/ 1.0 N) (/ 0.5 (* N N)))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))) (cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))))
140.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
140.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))
136.0ms	(cbrt (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify1.2s

Counts

191 → 191

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	479	10597
1	1065	9575
2	2847	8385
done	5001	8283

prune532.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

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

bsearch34.0ms

Steps

Iters	Range		Point
9	0.08347146558812443	2231369.5462890854	9562.64518051556

simplify4.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	41
1	33	39
2	38	39
done	38	39

end0.0ms

sample1.3s

Algorithm

intervals

Results

439.0ms	1787×	body	1280	valid
196.0ms	1261×	body	640	valid
188.0ms	7984×	body	80	nan
164.0ms	4035×	body	80	valid
60.0ms	611×	body	320	valid
19.0ms	306×	body	160	valid