Details

sample300.0ms

Algorithm

intervals

Results

116.0ms	89×	body	1280	valid
106.0ms	35×	body	2560	valid
26.0ms	46×	body	640	valid
10.0ms	33×	body	320	valid
8.0ms	86×	body	80	valid
5.0ms	73×	body	80	nan
1.0ms	7×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.9b

localize18.0ms

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))

rewrite1.5s

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)))
228.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms	(pow (+ 1.0 (/ i n)) n)
389.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

548.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
348.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
334.0ms	(pow (+ 1.0 (/ i n)) n)
519.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.7s

Counts

333 → 333

Iterations

Iter	Nodes
done	5001
1	1521
0	479

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize54.0ms

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)))
8.2b	(* (* 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))

rewrite152.0ms

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:

1.0ms	(fma (* i i) 0.5 (* 1.0 i))
55.0ms	(* 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))
42.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

series929.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(fma (* i i) 0.5 (* 1.0 i))
332.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
246.0ms	(* (* 0.5 (log 1.0)) (* i i))
259.0ms	(/ (- (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

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.8b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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-l`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/r` `div-exp` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `unswap-sqr` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `flip--`

Counts

4 → 113

Calls

4 calls:

19.0ms	(* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n)
49.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n))
20.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
21.0ms	(* (* 0.5 (log 1.0)) (* i i))

series1.0s

Counts

4 → 12

Calls

4 calls:

285.0ms	(* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n)
268.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i) n))
207.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
255.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify2.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5002
2	3009
1	563
0	204

prune840.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.8b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
12.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
27.0ms	(* (* 0.5 (log 1.0)) (* i i))

series890.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(cbrt n)
228.0ms	(cbrt n)
195.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) i)
218.0ms	(* (* 0.5 (log 1.0)) (* i i))

simplify1.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1866
1	347
0	140

prune536.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.8b

regimes655.0ms

Accuracy

53.1% (10.7b remaining)

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

bsearch282.0ms

Steps

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

simplify9.0ms

Iterations

Iter	Nodes
done	43
1	43
0	31

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.6s	2469×	body	1280	valid
2.4s	962×	body	2560	valid
686.0ms	1584×	body	640	valid
569.0ms	878×	body	320	valid
273.0ms	3111×	body	80	valid
153.0ms	2251×	body	80	nan
115.0ms	451×	body	160	valid
44.0ms	11×	body	5120	valid