Details

sample272.0ms

Algorithm

intervals

Results

104.0ms	89×	body	1280	valid
101.0ms	35×	body	2560	valid
24.0ms	46×	body	640	valid
10.0ms	33×	body	320	valid
6.0ms	86×	body	80	valid
4.0ms	73×	body	80	nan
2.0ms	7×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	414
1	25	414
2	60	414
3	144	414
4	364	414
5	1593	414
done	5000	414

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize32.0ms

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)
5.3b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite996.0ms

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:

397.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
182.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms	(pow (+ 1.0 (/ i n)) n)
376.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

552.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
366.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
264.0ms	(pow (+ 1.0 (/ i n)) n)
452.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.0s

Counts

333 → 333

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	479	209690
1	1521	198364
done	5001	192014

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
8.2b	(* (* i i) (log 1.0))
18.8b	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
97×	`add-sqr-sqrt`
86×	`*-un-lft-identity` `add-cube-cbrt`
51×	`associate-r`
28×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
13×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod` `div-inv`
7×	`pow-prod-down`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `log-pow` `flip--`

Counts

4 → 192

Calls

4 calls:

23.0ms	(* (* i i) 0.5)
28.0ms	(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
26.0ms	(* (* i i) (log 1.0))
22.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

series812.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* i i) 0.5)
263.0ms	(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
271.0ms	(* (* i i) (log 1.0))
243.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

simplify1.7s

Counts

204 → 204

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	336	113638
1	1033	107741
done	5001	105888

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
0.1b	(* 100.0 (* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
7.7b	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
8.2b	(* (* i i) (log 1.0))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
17×	`pow1` `associate-l`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-r`
7×	`pow-prod-down`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `cbrt-undiv` `associate-/r` `distribute-lft-in` `div-exp` `-commutative` `associate-/l*` `unswap-sqr`
2×	`associate-*l/` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

30.0ms	(* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
42.0ms	(* 100.0 (* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
22.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
28.0ms	(* (* i i) (log 1.0))

series935.0ms

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
296.0ms	(* 100.0 (* (/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
197.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
196.0ms	(* (* i i) (log 1.0))

simplify2.8s

Counts

129 → 129

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	214	64114
1	585	60789
2	3214	59801
done	5002	59621

prune628.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
7.7b	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
8.2b	(* (* i i) (log 1.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
12.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
15.0ms	(* (* i i) (log 1.0))

series719.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt n)
202.0ms	(cbrt n)
155.0ms	(/ (- (fma (log 1.0) n (fma 1.0 i (* (* i i) 0.5))) (* (* (* i i) (log 1.0)) 0.5)) i)
157.0ms	(* (* i i) (log 1.0))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	150	34157
1	369	32145
2	2069	30265
done	5001	29845

prune496.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.8b

regimes460.0ms

Accuracy

53.1% (10.7b remaining)

Error of 21.7b against oracle of 11.0b and baseline of 33.8b

bsearch242.0ms

Steps

Iters	Range		Point
9	3.0812599035097804e-09	7.830610238325062	4.039962480132393
9	-69051.06592837533	-4.7512835972832904e-05	-0.008529206764181105

simplify12.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	31	1258
1	43	1258
done	43	1258

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.4s	962×	body	2560	valid
2.3s	2469×	body	1280	valid
617.0ms	1584×	body	640	valid
230.0ms	3111×	body	80	valid
180.0ms	878×	body	320	valid
153.0ms	2251×	body	80	nan
60.0ms	451×	body	160	valid
38.0ms	11×	body	5120	valid