Details

sample236.0ms

Algorithm

intervals

Results

85.0ms	83×	body	1280	valid
61.0ms	22×	body	2560	valid
28.0ms	51×	body	640	valid
13.0ms	35×	body	320	valid
10.0ms	110×	body	80	valid
7.0ms	76×	body	80	nan
2.0ms	8×	body	160	valid

simplify3.3s

Counts: 1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize19.0ms

Local error

Found 3 expressions with local error:

8.5b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
4.9b	(pow (+ 1 (/ i n)) n)
0.1b	(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite28.0ms

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:

Slowest

16.0ms	(pow (+ 1 (/ i n)) n)
11.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
0.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)

series1.1s

Counts

3 → 9

Calls

3 calls:

Slowest

472.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
356.0ms	(pow (+ 1 (/ i n)) n)
303.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)

simplify1.7s

Counts: 114 → 114

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize18.0ms

Local error

Found 4 expressions with local error:

8.6b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
8.6b	(* n (log1p (/ i n)))
4.4b	(log1p (/ i n))
2.3b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite18.0ms

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:

Slowest

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

series881.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

431.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
303.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
78.0ms	(* n (log1p (/ i n)))
68.0ms	(log1p (/ i n))

simplify1.2s

Counts: 129 → 129

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.8b

localize23.0ms

Local error

Found 4 expressions with local error:

8.6b	(* n (log1p (/ i n)))
4.4b	(log1p (/ i n))
2.3b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.1b	(/ (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) (/ 1 n))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

421×	`times-frac`
204×	`add-sqr-sqrt`
202×	`*-un-lft-identity` `add-cube-cbrt`
29×	`div-inv`
28×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`div-exp`
13×	`associate-/r` `associate-/l`
8×	`cbrt-undiv`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`rec-exp` `1-exp`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `associate-/r/` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 266

Calls

4 calls:

Slowest

19.0ms	(/ (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) (/ 1 n))
13.0ms	(* n (log1p (/ i n)))
1.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series886.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

437.0ms	(/ (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) (/ 1 n))
293.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
91.0ms	(* n (log1p (/ i n)))
65.0ms	(log1p (/ i n))

simplify925.0ms

Counts: 278 → 278

prune2.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.8b

localize40.0ms

Local error

Found 4 expressions with local error:

46.2b	(posit16->real (real->posit16 (log1p (/ i n))))
8.6b	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
4.4b	(log1p (/ i n))
2.3b	(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `fma-udef` `remove-posit16` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

Slowest

6.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
0.0ms	(log1p (/ i n))
0.0ms	(posit16->real (real->posit16 (log1p (/ i n))))
0.0ms	(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)

series443.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

258.0ms	(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)
67.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
63.0ms	(posit16->real (real->posit16 (log1p (/ i n))))
56.0ms	(log1p (/ i n))

simplify1.5s

Counts: 67 → 67

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.8b

regimes234.0ms

Accuracy

45.3% (13.2b remaining)

Error of 26.7b against oracle of 13.5b and baseline of 37.7b

bsearch740.0ms

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.4s	2444×	body	1280	valid
2.8s	1011×	body	2560	valid
1.1s	1612×	body	640	valid
409.0ms	3010×	body	80	valid
339.0ms	871×	body	320	valid
307.0ms	2279×	body	80	nan
136.0ms	460×	body	160	valid
37.0ms	8×	body	5120	valid