Details

sample311.0ms

Algorithm

intervals

Results

133.0ms	95×	body	1280	valid
83.0ms	26×	body	2560	valid
32.0ms	48×	body	640	valid
12.0ms	101×	body	80	valid
11.0ms	26×	body	320	valid
9.0ms	80×	body	80	nan
8.0ms	2×	body	5120	valid
5.0ms	17×	body	160	valid

simplify527.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	533
3	154
2	59
1	28
0	10

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(fma 100 (pow (+ 1 (/ i n)) n) -100)
6.8b	(pow (+ 1 (/ i n)) n)
11.9b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
49×	`*-un-lft-identity`
47×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-exp-log`
8×	`add-cbrt-cube`
5×	`div-inv`
4×	`pow1` `unpow-prod-down`
3×	`expm1-log1p-u` `cbrt-undiv` `pow-unpow` `div-exp` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
1×	`pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `pow-exp` `associate-/r/` `fma-udef` `distribute-lft-out` `sqr-pow`

Counts

3 → 105

Calls

3 calls:

0.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
9.0ms	(pow (+ 1 (/ i n)) n)
6.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series960.0ms

Counts

3 → 9

Calls

3 calls:

326.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
289.0ms	(pow (+ 1 (/ i n)) n)
345.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify952.0ms

Counts

114 → 114

Iterations

Iter	Nodes
done	2005
2	1605
1	528
0	222

prune611.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.5b

localize30.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
5.6b	(log1p (/ i n))
11.6b	(* n (log1p (/ i n)))
11.9b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/l*`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
1.0ms	(log1p (/ i n))
7.0ms	(* n (log1p (/ i n)))
9.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

series868.0ms

Counts

4 → 12

Calls

4 calls:

309.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
57.0ms	(log1p (/ i n))
79.0ms	(* n (log1p (/ i n)))
422.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

simplify612.0ms

Counts

129 → 129

Iterations

Iter	Nodes
done	2000
1	636
0	257

prune627.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize19.0ms

Local error

Found 4 expressions with local error:

2.7b	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
5.6b	(log1p (/ i n))
11.6b	(* n (log1p (/ i n)))
11.9b	(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
5×	`expm1-log1p-u` `div-inv`
4×	`insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `log1p-udef` `clear-num` `sum-log` `fma-def` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

9.0ms	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))
28.0ms	(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))

series736.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
56.0ms	(log1p (/ i n))
63.0ms	(* n (log1p (/ i n)))
365.0ms	(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))

simplify528.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2000
1	720
0	272

prune523.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize47.0ms

Local error

Found 4 expressions with local error:

11.6b	(* n (log1p (/ i n)))
11.6b	(* n (log1p (/ i n)))
11.6b	(* n (log1p (/ i n)))
11.9b	(/ (/ (fma 1000000 (* (exp (* n (log1p (/ i n)))) (* (exp (* n (log1p (/ i n)))) (exp (* n (log1p (/ i n)))))) -1000000) (fma (* 100 (exp (* n (log1p (/ i n))))) (* 100 (exp (* n (log1p (/ i n))))) (* -100 (- -100 (* 100 (exp (* n (log1p (/ i n))))))))) (/ i n))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

421×	`times-frac`
212×	`add-sqr-sqrt`
206×	`*-un-lft-identity` `add-cube-cbrt`
29×	`div-inv`
22×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r` `associate-/l`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/r/` `associate-/l/`

Counts

4 → 281

Calls

4 calls:

12.0ms	(* n (log1p (/ i n)))
6.0ms	(* n (log1p (/ i n)))
6.0ms	(* n (log1p (/ i n)))
9.0ms	(/ (/ (fma 1000000 (* (exp (* n (log1p (/ i n)))) (* (exp (* n (log1p (/ i n)))) (exp (* n (log1p (/ i n)))))) -1000000) (fma (* 100 (exp (* n (log1p (/ i n))))) (* 100 (exp (* n (log1p (/ i n))))) (* -100 (- -100 (* 100 (exp (* n (log1p (/ i n))))))))) (/ i n))

series6.3s

Counts

4 → 12

Calls

4 calls:

72.0ms	(* n (log1p (/ i n)))
87.0ms	(* n (log1p (/ i n)))
75.0ms	(* n (log1p (/ i n)))
6.1s	(/ (/ (fma 1000000 (* (exp (* n (log1p (/ i n)))) (* (exp (* n (log1p (/ i n)))) (exp (* n (log1p (/ i n)))))) -1000000) (fma (* 100 (exp (* n (log1p (/ i n))))) (* 100 (exp (* n (log1p (/ i n))))) (* -100 (- -100 (* 100 (exp (* n (log1p (/ i n))))))))) (/ i n))

simplify1.3s

Counts

293 → 293

Iterations

Iter	Nodes
done	2001
1	1467
0	485

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

regimes266.0ms

Accuracy

54% (11.9b remaining)

Error of 25.6b against oracle of 13.7b and baseline of 39.6b

bsearch1.4s

Steps

Iters	Range		Point
5	1.028088151699927e+297	2.1345817878143117e+297	1.3330696406606884e+297
8	7.041325302301213e+252	7.326822544245665e+255	2.1565169088621677e+254
9	6.927539149538789e-07	0.5242927222148749	0.06286762942468366
8	1.1847563049182468e-191	2.2753319120576038e-187	1.2043330665713129e-191
3	6.659097204475327e-206	8.137592765991024e-206	8.045186793396293e-206
6	-6.493281180427814e-218	-1.272279862751547e-218	-5.102830896109795e-218
8	-6.101874035407836e-196	-8.194216137782486e-199	-4.745225464100608e-198
9	-1.2862858880804409e-14	-2.4564544670811215e-20	-1.1676448974447302e-14

simplify86.0ms

Iterations

Iter	Nodes
done	114
1	114
0	87

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.2s	2542×	body	1280	valid
2.7s	948×	body	2560	valid
959.0ms	1614×	body	640	valid
419.0ms	854×	body	320	valid
340.0ms	3023×	body	80	valid
276.0ms	2178×	body	80	nan
98.0ms	440×	body	160	valid
81.0ms	14×	body	5120	valid