Details

sample234.0ms

Algorithm

intervals

Results

97.0ms	87×	body	1280	valid
65.0ms	24×	body	2560	valid
27.0ms	52×	body	640	valid
10.0ms	32×	body	320	valid
7.0ms	93×	body	80	valid
5.0ms	80×	body	80	nan
4.0ms	19×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1593
4	364
3	144
2	60
1	25
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative`

Counts

4 → 321

Calls

4 calls:

391.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
213.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
464.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

583.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
379.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
323.0ms	(pow (+ 1.0 (/ i n)) n)
521.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.9s

Counts

333 → 333

Iterations

Iter	Nodes
done	5001
1	1521
0	479

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
0.1b	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
12.1b	(* (* 0.5 (log 1.0)) (* i i))
18.2b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
91×	`add-sqr-sqrt`
82×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-r`
30×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
13×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `fma-udef` `flip--`

Counts

4 → 177

Calls

4 calls:

0.0ms	(fma (* i i) 0.5 (* 1.0 i))
42.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
44.0ms	(* (* 0.5 (log 1.0)) (* i i))
31.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

series793.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (* i i) 0.5 (* 1.0 i))
220.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
241.0ms	(* (* 0.5 (log 1.0)) (* i i))
248.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

simplify1.3s

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	972
0	314

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
0.1b	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n))
11.5b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
12.1b	(* (* 0.5 (log 1.0)) (* i i))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-cbrt-cube` `add-exp-log`
21×	`pow1`
13×	`add-sqr-sqrt` `*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
11×	`pow-prod-down`
9×	`times-frac`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `associate-r` `*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-l/` `associate-r/` `fma-udef` `div-inv` `flip--`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (* i i) 0.5 (* 1.0 i))
41.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n))
12.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
28.0ms	(* (* 0.5 (log 1.0)) (* i i))

series684.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma (* i i) 0.5 (* 1.0 i))
240.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n))
162.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
188.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify2.0s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2685
1	484
0	182

prune543.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

localize48.0ms

Local error

Found 4 expressions with local error:

12.1b	(* (* 0.5 (log 1.0)) (* i i))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`cbrt-prod`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 69

Calls

4 calls:

25.0ms	(* (* 0.5 (log 1.0)) (* i i))
2.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
2.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
2.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))

series9.3s

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (* 0.5 (log 1.0)) (* i i))
3.2s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
2.9s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))
3.0s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))))

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1410
1	297
0	114

prune479.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

regimes277.0ms

Accuracy

52.6% (10.8b remaining)

Error of 22.2b against oracle of 11.4b and baseline of 34.2b

bsearch326.0ms

Steps

Iters	Range		Point
7	7.2949686944817395e+205	1.8280591761267005e+208	1.540498293983816e+208
12	9.084828359643272e-19	1.6311032011848909e+25	1.9432388931584246
5	-7.642915086960539e-08	-3.0023583529873386e-08	-7.524185979796087e-08

simplify16.0ms

Iterations

Iter	Nodes
done	63
1	63
0	50

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.2s	2441×	body	1280	valid
1.9s	972×	body	2560	valid
602.0ms	1619×	body	640	valid
208.0ms	3005×	body	80	valid
173.0ms	920×	body	320	valid
117.0ms	2297×	body	80	nan
80.0ms	453×	body	160	valid
32.0ms	9×	body	5120	valid