Details

sample208.0ms

Algorithm

intervals

Results

73.0ms	79×	body	1280	valid
70.0ms	28×	body	2560	valid
25.0ms	54×	body	640	valid
8.0ms	32×	body	320	valid
7.0ms	99×	body	80	valid
3.0ms	58×	body	80	nan
2.0ms	13×	body	160	valid

simplify2.1s

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: 41.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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:

442.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
221.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms	(pow (+ 1.0 (/ i n)) n)
490.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

510.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
324.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
276.0ms	(pow (+ 1.0 (/ i n)) n)
463.0ms	(/ (- (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

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize57.0ms

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)))
8.9b	(* (* 0.5 (log 1.0)) (* i i))
15.2b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

rewrite121.0ms

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))
39.0ms	(* 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))

series810.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(fma (* i i) 0.5 (* 1.0 i))
235.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
242.0ms	(* (* 0.5 (log 1.0)) (* i i))
247.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

simplify1.2s

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	972
0	314

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) 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)
8.4b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
8.9b	(* (* 0.5 (log 1.0)) (* i i))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
26×	`add-sqr-sqrt`
23×	`pow1`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
17×	`associate-r`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `-commutative` `associate-/l*`
2×	`associate-*r/` `div-inv` `unswap-sqr` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*l/` `flip--`

Counts

4 → 113

Calls

4 calls:

19.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i))
35.0ms	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)) n)
13.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
41.0ms	(* (* 0.5 (log 1.0)) (* i i))

series832.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i))
247.0ms	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)) n)
195.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
204.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify2.4s

Counts

125 → 125

Iterations

Iter	Nodes
done	5002
2	3321
1	571
0	202

prune750.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 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))) (/ 1 i))) n)
8.6b	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i))
8.9b	(* (* 0.5 (log 1.0)) (* i i))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
44×	`add-cbrt-cube`
36×	`prod-exp`
32×	`pow1`
24×	`cbrt-unprod`
21×	`add-sqr-sqrt`
18×	`associate-r` `pow-prod-down`
15×	`-un-lft-identity` `associate-r/`
14×	`add-cube-cbrt`
12×	`associate-*l/`
11×	`times-frac`
8×	`associate-l`
6×	`frac-times` `flip3--` `div-exp` `flip--`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `un-div-inv` `unswap-sqr`
1×	`div-inv`

Counts

4 → 129

Calls

4 calls:

32.0ms	(* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i)))
117.0ms	(* (* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i))) n)
30.0ms	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i))
23.0ms	(* (* 0.5 (log 1.0)) (* i i))

series761.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i)))
214.0ms	(* (* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i))) n)
164.0ms	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ 1 i))
215.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify1.0s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
1	688
0	236

prune839.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

regimes208.0ms

Accuracy

42.1% (13.1b remaining)

Error of 24.3b against oracle of 11.2b and baseline of 33.8b

bsearch320.0ms

Steps

Iters	Range		Point
10	-8.507001710182289e-307	8.575654121239942e-297	8.43948162108991e-297
5	-2.085807323628561e+25	-8.665460962243007e+24	-1.5240705750258725e+25
8	-1.3111623360014479e+36	-4.953784207856335e+31	-4.995965210525052e+35
6	-4.468344328437476e+60	-4.544149282436552e+59	-5.46477309603401e+59

simplify10.0ms

Iterations

Iter	Nodes
done	51
1	51
0	39

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.4s	2575×	body	1280	valid
2.2s	917×	body	2560	valid
704.0ms	1578×	body	640	valid
501.0ms	3075×	body	80	valid
272.0ms	879×	body	320	valid
135.0ms	2237×	body	80	nan
66.0ms	457×	body	160	valid
44.0ms	9×	body	5120	valid