Details

sample325.0ms

Algorithm

intervals

Results

128.0ms	85×	body	1280	valid
88.0ms	28×	body	2560	valid
54.0ms	52×	body	640	valid
13.0ms	97×	body	80	valid
12.0ms	26×	body	320	valid
8.0ms	69×	body	80	nan
5.0ms	16×	body	160	valid

simplify4.4s

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.8b

localize15.0ms

Local error

Found 3 expressions with local error:

8.7b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
6.7b	(pow (+ 1 (/ i n)) n)
2.0b	(fma 100 (pow (+ 1 (/ i n)) n) -100)

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:

Slowest

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

series916.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

386.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
301.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
228.0ms	(pow (+ 1 (/ i n)) n)

simplify1.8s

Counts: 114 → 114

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

8.8b	(* n (log1p (/ i n)))
8.7b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
5.4b	(log1p (/ i n))
3.7b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite24.0ms

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

12.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
8.0ms	(* n (log1p (/ i n)))
1.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series959.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

477.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
311.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
99.0ms	(log1p (/ i n))
71.0ms	(* n (log1p (/ i n)))

simplify910.0ms

Counts: 129 → 129

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize26.0ms

Local error

Found 4 expressions with local error:

8.8b	(* n (log1p (/ i n)))
5.4b	(log1p (/ i n))
3.7b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.1b	(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`times-frac`
8×	`pow1`
6×	`associate-r`
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` `associate-*l/` `log1p-expm1` `fma-udef` `div-inv`

Counts

4 → 79

Calls

4 calls:

Slowest

10.0ms	(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
6.0ms	(* n (log1p (/ i n)))
0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series790.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

378.0ms	(* (/ (fma 100 (exp (* n (log1p (/ i n)))) -100) i) n)
260.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
80.0ms	(log1p (/ i n))
72.0ms	(* n (log1p (/ i n)))

simplify2.3s

Counts: 91 → 91

prune681.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize42.0ms

Local error

Found 4 expressions with local error:

45.4b	(posit16->real (real->posit16 (log1p (/ i n))))
8.8b	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
5.4b	(log1p (/ i n))
3.7b	(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)

series423.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

248.0ms	(fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100)
64.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
56.0ms	(log1p (/ i n))
55.0ms	(posit16->real (real->posit16 (log1p (/ i n))))

simplify1.5s

Counts: 67 → 67

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

regimes226.0ms

Accuracy

52.6% (11.7b remaining)

Error of 25.2b against oracle of 13.5b and baseline of 38.2b

bsearch856.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.5s	2511×	body	1280	valid
2.7s	974×	body	2560	valid
1.1s	1598×	body	640	valid
345.0ms	892×	body	320	valid
335.0ms	3047×	body	80	valid
287.0ms	2316×	body	80	nan
106.0ms	430×	body	160	valid
23.0ms	5×	body	5120	valid