Details

sample105.0ms

Algorithm

intervals

Results

33.0ms	62×	body	1280	valid
28.0ms	243×	body	80	nan
16.0ms	42×	body	640	valid
11.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize15.0ms

Local error

Found 1 expressions with local error:

2.5b	(- (log1p N) (log N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

12.0ms

(- (log1p N) (log N))

series97.0ms

Counts

1 → 3

Calls

1 calls:

96.0ms

(- (log1p N) (log N))

simplify1.4s

Counts

40 → 40

Iterations

Iter	Nodes
4	2678
3	962
2	372
1	184
0	83

prune328.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/3 N) (* N N))
0.2b	(/ -1/2 (* N N))
0.3b	(/ 1/3 N)
11.6b	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
37×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
7×	`fma-def` `div-inv`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `pow1` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+r+` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

10.0ms	(/ (/ 1/3 N) (* N N))
6.0ms	(/ -1/2 (* N N))
4.0ms	(/ 1/3 N)
101.0ms	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (/ 1/3 N) (* N N))
50.0ms	(/ -1/2 (* N N))
28.0ms	(/ 1/3 N)
35.0ms	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))

simplify1.0s

Counts

144 → 144

Iterations

Iter	Nodes
2	2273
1	576
0	209

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

11.6b	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))
19.2b	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
19.2b	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
19.2b	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
20×	`distribute-lft-out`
18×	`cbrt-prod`
16×	`frac-add`
15×	`cbrt-div`
9×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
8×	`flip3-+` `flip-+`
7×	`fma-def`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sum-log` `times-frac` `pow1/3`
1×	`+-commutative` `associate-+r+`

Counts

4 → 95

Calls

4 calls:

56.0ms	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))
53.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
62.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
76.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N))))
77.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
98.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))
73.0ms	(cbrt (+ (/ -1/2 (* N N)) (+ (/ 1 N) (/ (/ 1/3 N) (* N N)))))

simplify8.7s

Counts

107 → 107

Iterations

Iter	Nodes
3	7585
2	1604
1	410
0	143

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
2.4b	(log (/ (+ 1 N) N))

rewrite36.0ms

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` `insert-posit16` `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 → 66

Calls

2 calls:

27.0ms	(/ (+ 1 N) N)
8.0ms	(log (/ (+ 1 N) N))

series111.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (+ 1 N) N)
45.0ms	(log (/ (+ 1 N) N))

simplify4.1s

Counts

72 → 72

Iterations

Iter	Nodes
4	5667
3	1564
2	510
1	231
0	106

prune624.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch44.0ms

Steps

Iters	Range		Point
9	3862.7483140020904	25612678030.77693	6613.323166361232

simplify5.0ms

Iterations

Iter	Nodes
2	22
1	22
0	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1779×	body	1280	valid
632.0ms	7976×	body	80	nan
477.0ms	4061×	body	80	valid
461.0ms	1289×	body	640	valid
193.0ms	573×	body	320	valid
46.0ms	298×	body	160	valid