Details

sample234.0ms

Algorithm

intervals

Results

101.0ms	39×	body	2560	valid
68.0ms	76×	body	1280	valid
27.0ms	61×	body	640	valid
7.0ms	27×	body	320	valid
5.0ms	90×	body	80	valid
3.0ms	64×	body	80	nan
2.0ms	12×	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: 44.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.1b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.0s

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:

407.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
370.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts

4 → 12

Calls

4 calls:

591.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
441.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
341.0ms	(pow (+ 1.0 (/ i n)) n)
514.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.6s

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: 23.8b

localize53.0ms

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)))
10.9b	(* (* 0.5 (log 1.0)) (* i i))
18.8b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

rewrite132.0ms

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))
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)))
39.0ms	(* (* 0.5 (log 1.0)) (* i i))
41.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

series956.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma (* i i) 0.5 (* 1.0 i))
264.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
298.0ms	(* (* 0.5 (log 1.0)) (* i i))
283.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

simplify1.4s

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	972
0	314

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
2.2b	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
10.9b	(* (* (* i i) 0.5) (log 1.0))
11.6b	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log`
45×	`add-cbrt-cube`
40×	`prod-exp`
30×	`pow1`
24×	`cbrt-unprod`
20×	`associate-l`
19×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`pow-prod-down`
12×	`associate-*l/`
9×	`times-frac` `associate-r` `associate-*r/`
8×	`div-exp`
6×	`log-prod`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `rec-exp` `1-exp` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
1×	`log-pow` `div-inv` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

88.0ms	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
21.0ms	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
60.0ms	(* (* (* i i) 0.5) (log 1.0))
33.0ms	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

series1.2s

Counts

4 → 12

Calls

4 calls:

253.0ms	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
193.0ms	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
201.0ms	(* (* (* i i) 0.5) (log 1.0))
577.0ms	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

simplify1.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
1	761
0	253

prune856.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma i 0.5 1.0) i)
0.1b	(* 100.0 (* (/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i) n))
10.2b	(/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i)
10.9b	(* (log 1.0) (* (* i i) 0.5))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

10.0ms	(* (fma i 0.5 1.0) i)
47.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i) n))
27.0ms	(/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i)
50.0ms	(* (log 1.0) (* (* i i) 0.5))

series692.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (fma i 0.5 1.0) i)
234.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i) n))
184.0ms	(/ (- (fma n (log 1.0) (* (fma i 0.5 1.0) i)) (* (log 1.0) (* (* i i) 0.5))) i)
187.0ms	(* (log 1.0) (* (* i i) 0.5))

simplify2.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	2608
1	518
0	198

prune626.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.5b

regimes385.0ms

Accuracy

55% (10.3b remaining)

Error of 21.4b against oracle of 11.1b and baseline of 34.0b

bsearch658.0ms

Steps

Iters	Range		Point
9	7.674138475383248	1698412.1750747235	11.911866918652608
10	1.748216843554884e-276	2.202367239653683e-265	4.681047647742426e-271
10	-3.124575090294561e-11	-2.0990955826697636e-21	-3.0764933618318215e-11

simplify17.0ms

Iterations

Iter	Nodes
done	73
1	73
0	55

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.4s	2448×	body	1280	valid
2.2s	967×	body	2560	valid
809.0ms	1652×	body	640	valid
530.0ms	867×	body	320	valid
218.0ms	3015×	body	80	valid
181.0ms	2204×	body	80	nan
59.0ms	409×	body	160	valid
44.0ms	10×	body	5120	valid