Details

sample309.0ms

Algorithm

intervals

Results

110.0ms	80×	body	1280	valid
102.0ms	31×	body	2560	valid
39.0ms	53×	body	640	valid
13.0ms	104×	body	80	valid
12.0ms	26×	body	320	valid
8.0ms	72×	body	80	nan
6.0ms	20×	body	160	valid

simplify823.0ms

Counts: 1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.7b

localize24.0ms

Local error

Found 3 expressions with local error:

10.2b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
6.1b	(pow (+ 1 (/ i n)) n)
0.8b	(fma 100 (pow (+ 1 (/ i n)) n) -100)

rewrite22.0ms

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

14.0ms	(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)

series1.0s

Counts

3 → 9

Calls

3 calls:

Slowest

415.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))
330.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
264.0ms	(pow (+ 1 (/ i n)) n)

simplify620.0ms

Counts: 159 → 114

prune978.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
10.0b	(* n (log1p (/ i n)))
5.8b	(log1p (/ i n))
2.4b	(fma 100 (exp (* n (log1p (/ i n)))) -100)

rewrite20.0ms

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

9.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
8.0ms	(* n (log1p (/ i n)))
0.0ms	(log1p (/ i n))
0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)

series950.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

513.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
286.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
88.0ms	(* n (log1p (/ i n)))
63.0ms	(log1p (/ i n))

simplify358.0ms

Counts: 168 → 129

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize31.0ms

Local error

Found 4 expressions with local error:

10.2b	(/ (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ i n))
10.0b	(* n (log1p (/ i n)))
10.0b	(* n (log1p (/ i n)))
10.0b	(* n (log1p (/ i n)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
65×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-exp-log`
14×	`cbrt-prod`
13×	`associate-/r*` `add-cbrt-cube`
10×	`pow1`
9×	`associate-r` `associate-l`
6×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/r/`

Counts

4 → 150

Calls

4 calls:

Slowest

16.0ms	(/ (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ i n))
11.0ms	(* n (log1p (/ i n)))
10.0ms	(* n (log1p (/ i n)))
10.0ms	(* n (log1p (/ i n)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

469.0ms	(/ (cbrt (* (* (fma 100 (exp (* n (log1p (/ i n)))) -100) (fma 100 (exp (* n (log1p (/ i n)))) -100)) (fma 100 (exp (* n (log1p (/ i n)))) -100))) (/ i n))
71.0ms	(* n (log1p (/ i n)))
70.0ms	(* n (log1p (/ i n)))
65.0ms	(* n (log1p (/ i n)))

simplify867.0ms

Counts: 215 → 162

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.2b

localize33.0ms

Local error

Found 4 expressions with local error:

10.0b	(* n (log1p (/ i n)))
10.0b	(* n (log1p (/ i n)))
10.0b	(* n (log1p (/ i n)))
5.8b	(log1p (/ i n))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

Slowest

6.0ms	(* n (log1p (/ i n)))
6.0ms	(* n (log1p (/ i n)))
6.0ms	(* n (log1p (/ i n)))
0.0ms	(log1p (/ i n))

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(* n (log1p (/ i n)))
67.0ms	(* n (log1p (/ i n)))
66.0ms	(* n (log1p (/ i n)))
55.0ms	(log1p (/ i n))

simplify456.0ms

Counts: 86 → 87

prune933.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

regimes175.0ms

Accuracy

45.9% (14.1b remaining)

Error of 27.4b against oracle of 13.4b and baseline of 39.3b

bsearch967.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.5s	2450×	body	1280	valid
2.3s	964×	body	2560	valid
1.2s	1623×	body	640	valid
461.0ms	2268×	body	80	nan
339.0ms	3139×	body	80	valid
328.0ms	869×	body	320	valid
95.0ms	468×	body	160	valid
25.0ms	6×	body	5120	valid