Details

sample297.0ms

Algorithm

intervals

Results

106.0ms	37×	body	2560	valid
105.0ms	70×	body	1280	valid
38.0ms	57×	body	640	valid
14.0ms	35×	body	320	valid
9.0ms	83×	body	80	valid
6.0ms	62×	body	80	nan
3.0ms	12×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	2617
4	533
3	154
2	59
1	28
0	10

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize19.0ms

Local error

Found 3 expressions with local error:

2.4b	(fma 100 (pow (+ 1 (/ i n)) n) -100)
4.6b	(pow (+ 1 (/ i n)) n)
11.4b	(/ (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))

series1.0s

Counts

3 → 9

Calls

3 calls:

317.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
258.0ms	(pow (+ 1 (/ i n)) n)
469.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1605
1	528
0	222

prune625.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.9b

localize39.0ms

Local error

Found 4 expressions with local error:

4.1b	(log1p (/ i n))
5.6b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
11.3b	(* n (log1p (/ i n)))
11.4b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

rewrite25.0ms

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:

1.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
10.0ms	(* n (log1p (/ i n)))
12.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

96.0ms	(log1p (/ i n))
367.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
105.0ms	(* n (log1p (/ i n)))
508.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

simplify2.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	5007
2	2186
1	637
0	257

prune771.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.5b

localize34.0ms

Local error

Found 4 expressions with local error:

4.1b	(log1p (/ i n))
5.6b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
11.3b	(* n (log1p (/ i n)))
12.2b	(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac`
8×	`pow1`
6×	`associate-l`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `log1p-udef` `div-exp` `log1p-expm1` `associate-*r/` `fma-udef` `div-inv`

Counts

4 → 79

Calls

4 calls:

0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
6.0ms	(* n (log1p (/ i n)))
13.0ms	(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))

series921.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(log1p (/ i n))
334.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
81.0ms	(* n (log1p (/ i n)))
446.0ms	(* (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ n i))

simplify1.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1651
1	449
0	182

prune459.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.5b

localize32.0ms

Local error

Found 4 expressions with local error:

4.1b	(log1p (/ i n))
5.6b	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
11.3b	(* n (log1p (/ i n)))
12.2b	(* (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ n i))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

0.0ms	(log1p (/ i n))
9.0ms	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
5.0ms	(* n (log1p (/ i n)))
42.0ms	(* (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ n i))

series929.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(log1p (/ i n))
339.0ms	(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
62.0ms	(* n (log1p (/ i n)))
459.0ms	(* (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ n i))

simplify2.1s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2105
1	536
0	201

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.5b

regimes242.0ms

Accuracy

55.1% (11.5b remaining)

Error of 24.8b against oracle of 13.3b and baseline of 38.9b

bsearch489.0ms

Steps

Iters	Range		Point
11	5.7104977308190605e-08	2.005999702236418e+22	0.07870893021680746
10	-0.0018335887134067947	-3.3545779559118727e-13	-5.972711572932587e-05

simplify32.0ms

Iterations

Iter	Nodes
done	82
1	82
0	58

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.7s	969×	body	2560	valid
2.7s	2449×	body	1280	valid
1.4s	1660×	body	640	valid
414.0ms	3052×	body	80	valid
312.0ms	850×	body	320	valid
243.0ms	2271×	body	80	nan
95.0ms	432×	body	160	valid
39.0ms	10×	body	5120	valid