Details

sample123.0ms

Algorithm

intervals

Results

37.0ms	62×	body	1280	valid
24.0ms	272×	body	80	nan
15.0ms	40×	body	640	valid
12.0ms	123×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize45.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
4.4b	(- (log (+ N 1.0)) (log N))

rewrite45.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

10.0ms	(log (+ N 1.0))
32.0ms	(- (log (+ N 1.0)) (log N))

series207.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(log (+ N 1.0))
143.0ms	(- (log (+ N 1.0)) (log N))

simplify7.9s

Counts

49 → 49

Iterations

Iter	Nodes
done	5021
4	4745
3	1572
2	522
1	215
0	103

prune530.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize151.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N))
0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.7b	(/ 0.5 (* N N))
11.4b	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

35×	`times-frac`
27×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `insert-posit16` `div-inv`
3×	`prod-exp` `frac-sub` `cbrt-unprod`
2×	`clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `diff-log` `frac-add` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `associate-/l/`

Counts

4 → 105

Calls

4 calls:

115.0ms	(+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N))
55.0ms	(/ (/ 0.3333333333333333 N) (* N N))
32.0ms	(/ 0.5 (* N N))
839.0ms	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N))
63.0ms	(/ (/ 0.3333333333333333 N) (* N N))
32.0ms	(/ 0.5 (* N N))
45.0ms	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))

simplify4.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1835
1	541
0	204

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize302.0ms

Local error

Found 4 expressions with local error:

11.4b	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))
20.2b	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
20.2b	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
20.2b	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
21×	`cbrt-prod`
15×	`cbrt-div`
12×	`frac-sub`
9×	`add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`add-cube-cbrt`
4×	`pow1` `flip3-+` `times-frac` `flip3--` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `flip--` `distribute-lft-out`
3×	`pow1/3`
2×	`diff-log`
1×	`sum-log` `sub-neg` `associate--l+`

Counts

4 → 85

Calls

4 calls:

811.0ms	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))
359.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
364.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
338.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))

series1.0s

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N)))
303.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
315.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))
320.0ms	(cbrt (- (+ (/ (/ 0.3333333333333333 N) (* N N)) (/ 1.0 N)) (/ 0.5 (* N N))))

simplify3.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1385
1	426
0	166

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 N) N)
4.8b	(log (/ (+ 1.0 N) N))

rewrite94.0ms

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` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

65.0ms	(/ (+ 1.0 N) N)
24.0ms	(log (/ (+ 1.0 N) N))

series227.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (+ 1.0 N) N)
151.0ms	(log (/ (+ 1.0 N) N))

simplify4.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	2249
2	620
1	242
0	109

prune615.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes196.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch37.0ms

Steps

Iters	Range		Point
6	3173.18146809654	23716.851585869685	11332.770353358372

simplify10.0ms

Iterations

Iter	Nodes
done	21
1	21
0	19

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.0s	1790×	body	1280	valid
838.0ms	4031×	body	80	valid
632.0ms	8083×	body	80	nan
482.0ms	1270×	body	640	valid
177.0ms	606×	body	320	valid
47.0ms	303×	body	160	valid