Details

sample280.0ms

Algorithm

intervals

Results

103.0ms	29×	body	2560	valid
97.0ms	80×	body	1280	valid
33.0ms	55×	body	640	valid
11.0ms	105×	body	80	valid
9.0ms	23×	body	320	valid
7.0ms	71×	body	80	nan
5.0ms	20×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	7548
5	1515
4	436
3	154
2	59
1	28
0	10

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.1b

localize15.0ms

Local error

Found 3 expressions with local error:

1.3b	(fma (pow (+ 1 (/ i n)) n) 100 -100)
7.5b	(pow (+ 1 (/ i n)) n)
9.7b	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite16.0ms

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

series943.0ms

Counts

3 → 9

Calls

3 calls:

289.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
263.0ms	(pow (+ 1 (/ i n)) n)
390.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
3	4952
2	1593
1	506
0	222

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.8b

localize17.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
6.6b	(log1p (/ i n))
9.8b	(* n (log1p (/ i n)))
9.9b	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))

rewrite17.0ms

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

series768.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
56.0ms	(log1p (/ i n))
63.0ms	(* n (log1p (/ i n)))
373.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))

simplify759.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2167
1	620
0	257

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.5b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
6.6b	(log1p (/ i n))
9.8b	(* n (log1p (/ i n)))
10.9b	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
58×	`add-sqr-sqrt`
47×	`associate-r`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`add-cbrt-cube`
8×	`pow1` `prod-exp`
7×	`div-exp`
6×	`associate-l` `unswap-sqr`
5×	`expm1-log1p-u`
4×	`cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv`
2×	`rec-exp` `1-exp` `pow-prod-down` `*-commutative`
1×	`log1p-udef` `log1p-expm1` `associate-*r/` `associate-/r/` `un-div-inv` `fma-udef`

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
0.0ms	(log1p (/ i n))
6.0ms	(* n (log1p (/ i n)))
14.0ms	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
55.0ms	(log1p (/ i n))
65.0ms	(* n (log1p (/ i n)))
376.0ms	(* (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ 1 (/ i n)))

simplify640.0ms

Counts

132 → 132

Iterations

Iter	Nodes
2	2140
1	734
0	276

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.5b

localize42.0ms

Local error

Found 4 expressions with local error:

6.6b	(log1p (/ i n))
9.8b	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
10.9b	(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
44.8b	(posit16->real (real->posit16 (log1p (/ i n))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
58×	`add-sqr-sqrt`
47×	`associate-r`
44×	`*-un-lft-identity`
42×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`add-cbrt-cube`
8×	`pow1` `prod-exp`
7×	`div-exp`
6×	`associate-l` `unswap-sqr`
5×	`expm1-log1p-u`
4×	`cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv`
2×	`rec-exp` `1-exp` `pow-prod-down` `*-commutative`
1×	`log1p-udef` `log1p-expm1` `associate-*r/` `associate-/r/` `un-div-inv` `remove-posit16`

Counts

4 → 120

Calls

4 calls:

0.0ms	(log1p (/ i n))
7.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
19.0ms	(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
0.0ms	(posit16->real (real->posit16 (log1p (/ i n))))

series702.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log1p (/ i n))
63.0ms	(* n (posit16->real (real->posit16 (log1p (/ i n)))))
500.0ms	(* (fma (exp (* n (posit16->real (real->posit16 (log1p (/ i n)))))) 100 -100) (/ 1 (/ i n)))
77.0ms	(posit16->real (real->posit16 (log1p (/ i n))))

simplify1.3s

Counts

132 → 132

Iterations

Iter	Nodes
3	3955
2	1406
1	576
0	229

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.5b

regimes401.0ms

Accuracy

39.5% (14.4b remaining)

Error of 27.9b against oracle of 13.4b and baseline of 37.3b

bsearch1.3s

Steps

Iters	Range		Point
6	4.621974518686793e+243	3.8737175555983145e+244	7.810496096004307e+243
8	4.478245262004958e-68	1.8579537361026283e-63	1.965651820956631e-65
8	-4.9430805128531437e-306	3.1534353510591667e-307	-7.6539834001623e-311
10	-8222859.820370512	-0.0001334991810227847	-2.103154135664
7	-4.9288675399412147e+27	-1.4528216466580178e+26	-3.763036538905304e+26
9	-5.838125449252488e+44	-1.1127525490258259e+37	-4.0425022022190223e+43
9	-1.8382394431088474e+197	-1.162038091363608e+188	-5.4638361325642236e+190

simplify62.0ms

Iterations

Iter	Nodes
2	120
1	120
0	87

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.9s	2525×	body	1280	valid
2.5s	945×	body	2560	valid
1.1s	1614×	body	640	valid
744.0ms	447×	body	160	valid
399.0ms	3032×	body	80	valid
336.0ms	871×	body	320	valid
220.0ms	2195×	body	80	nan
46.0ms	11×	body	5120	valid