Details

sample242.0ms

Algorithm

intervals

Results

82.0ms	79×	body	1280	valid
71.0ms	30×	body	2560	valid
28.0ms	52×	body	640	valid
11.0ms	102×	body	80	valid
7.0ms	20×	body	320	valid
6.0ms	66×	body	80	nan
4.0ms	19×	body	160	valid
4.0ms	1×	body	5120	valid

simplify4.8s

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: 42.7b

localize17.0ms

Local error

Found 3 expressions with local error:

1.1b	(fma (pow (+ 1 (/ i n)) n) 100 -100)
7.3b	(pow (+ 1 (/ i n)) n)
8.2b	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

rewrite35.0ms

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)
19.0ms	(pow (+ 1 (/ i n)) n)
13.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

series854.0ms

Counts

3 → 9

Calls

3 calls:

267.0ms	(fma (pow (+ 1 (/ i n)) n) 100 -100)
248.0ms	(pow (+ 1 (/ i n)) n)
339.0ms	(/ (fma (pow (+ 1 (/ i n)) n) 100 -100) (/ i n))

simplify2.1s

Counts

114 → 114

Iterations

Iter	Nodes
3	4952
2	1593
1	506
0	222

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
6.3b	(log1p (/ i n))
8.2b	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
8.4b	(* n (log1p (/ i n)))

rewrite26.0ms

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)
1.0ms	(log1p (/ i n))
12.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
10.0ms	(* n (log1p (/ i n)))

series909.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
69.0ms	(log1p (/ i n))
420.0ms	(/ (fma (exp (* n (log1p (/ i n)))) 100 -100) (/ i n))
90.0ms	(* n (log1p (/ i n)))

simplify736.0ms

Counts

129 → 129

Iterations

Iter	Nodes
2	2021
1	620
0	257

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize27.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma (exp (* n (log1p (/ i n)))) 100 -100)
6.3b	(log1p (/ i n))
7.7b	(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
8.4b	(* n (log1p (/ i n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/l*`
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` `associate-/r` `div-exp` `associate-r` `associate-l*`
1×	`log1p-udef` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

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

series1.6s

Counts

4 → 12

Calls

4 calls:

302.0ms	(fma (exp (* n (log1p (/ i n)))) 100 -100)
63.0ms	(log1p (/ i n))
1.1s	(/ (/ i n) (fma (exp (* n (log1p (/ i n)))) 100 -100))
81.0ms	(* n (log1p (/ i n)))

simplify3.2s

Counts

129 → 129

Iterations

Iter	Nodes
3	7110
2	1818
1	638
0	277

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ i n) n)
0.1b	(/ 1/100 n)
0.3b	(/ 1 (fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n))))
3.3b	(fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/l*`
15×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/r*`
7×	`div-inv`
6×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`rec-exp` `1-exp` `fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 148

Calls

4 calls:

8.0ms	(/ (/ i n) n)
8.0ms	(/ 1/100 n)
6.0ms	(/ 1 (fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n))))
0.0ms	(fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (/ i n) n)
17.0ms	(/ 1/100 n)
58.0ms	(/ 1 (fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n))))
44.0ms	(fma -1/200 (/ i n) (fma (/ (/ i n) n) 1/200 (/ 1/100 n)))

simplify1.4s

Counts

160 → 160

Iterations

Iter	Nodes
3	3998
2	1231
1	520
0	255

prune1.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 2.5b

regimes334.0ms

Accuracy

53.6% (9.1b remaining)

Error of 11.7b against oracle of 2.6b and baseline of 22.3b

bsearch280.0ms

Steps

Iters	Range		Point
7	0.10106394179147121	1.6697130628152668	1.5588973207876802
9	-250055.29886925383	-3.0421098639022524	-3.074115167804112

simplify37.0ms

Iterations

Iter	Nodes
2	79
1	79
0	63

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.1s	2555×	body	1280	valid
2.8s	989×	body	2560	valid
1.0s	1582×	body	640	valid
654.0ms	3043×	body	80	valid
330.0ms	848×	body	320	valid
276.0ms	2348×	body	80	nan
107.0ms	460×	body	160	valid
28.0ms	6×	body	5120	valid