Details

sample241.0ms

Algorithm

intervals

Results

109.0ms	87×	body	1280	valid
60.0ms	22×	body	2560	valid
22.0ms	37×	body	640	valid
11.0ms	33×	body	320	valid
11.0ms	106×	body	80	valid
8.0ms	83×	body	80	nan
4.0ms	1×	body	5120	valid
3.0ms	13×	body	160	valid

simplify5.2s

Counts: 1 → 1

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize16.0ms

Local error

Found 3 expressions with local error:

8.9b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
6.4b	(pow (+ 1 (/ i n)) n)
1.2b	(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite33.0ms

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

23.0ms	(pow (+ 1 (/ i n)) n)
7.0ms	(/ (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

447.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
343.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
312.0ms	(pow (+ 1 (/ i n)) n)

simplify2.0s

Counts: 114 → 114

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize18.0ms

Local error

Found 4 expressions with local error:

9.6b	(* n (log1p (/ i n)))
9.3b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
5.6b	(log1p (/ i n))
3.3b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

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:

Slowest

13.0ms	(* n (log1p (/ i n)))
10.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

560.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
357.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
87.0ms	(* n (log1p (/ i n)))
76.0ms	(log1p (/ i n))

simplify942.0ms

Counts: 129 → 129

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.7b

localize59.0ms

Local error

Found 4 expressions with local error:

45.6b	(posit16->real (real->posit16 (log1p (/ i n))))
9.6b	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
9.3b	(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
5.6b	(log1p (/ i n))

rewrite21.0ms

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` `remove-posit16` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

Slowest

10.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
8.0ms	(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
0.0ms	(posit16->real (real->posit16 (log1p (/ i n))))
0.0ms	(log1p (/ i n))

series809.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

574.0ms	(/ (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ i n))
92.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
74.0ms	(log1p (/ i n))
68.0ms	(posit16->real (real->posit16 (log1p (/ i n))))

simplify2.0s

Counts: 129 → 129

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.7b

localize50.0ms

Local error

Found 4 expressions with local error:

45.6b	(posit16->real (real->posit16 (log1p (/ i n))))
10.9b	(* (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ n i))
9.6b	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
5.6b	(log1p (/ i n))

rewrite30.0ms

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/` `div-inv` `remove-posit16`

Counts

4 → 79

Calls

4 calls:

Slowest

19.0ms	(* (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ n i))
9.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
1.0ms	(posit16->real (real->posit16 (log1p (/ i n))))
0.0ms	(log1p (/ i n))

series711.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

497.0ms	(* (fma 100 (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) -100) (/ n i))
82.0ms	(posit16->real (real->posit16 (log1p (/ i n))))
74.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
57.0ms	(log1p (/ i n))

simplify1.1s

Counts: 91 → 91

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

regimes292.0ms

Accuracy

43.4% (13.4b remaining)

Error of 27.0b against oracle of 13.6b and baseline of 37.3b

bsearch1.5s

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.1s	1006×	body	2560	valid
3.0s	2502×	body	1280	valid
1.1s	1610×	body	640	valid
369.0ms	3121×	body	80	valid
317.0ms	848×	body	320	valid
267.0ms	2301×	body	80	nan
98.0ms	410×	body	160	valid
32.0ms	7×	body	5120	valid