Details

sample228.0ms

Algorithm

intervals

Results

95.0ms	80×	body	1280	valid
74.0ms	28×	body	2560	valid
24.0ms	51×	body	640	valid
8.0ms	115×	body	80	valid
7.0ms	21×	body	320	valid
4.0ms	75×	body	80	nan
2.0ms	13×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	2617
4	533
3	154
2	59
1	28
0	10

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize32.0ms

Local error

Found 3 expressions with local error:

1.4b	(fma 100 (pow (+ 1 (/ i n)) n) -100)
6.1b	(pow (+ 1 (/ i n)) n)
10.2b	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite24.0ms

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 100 (pow (+ 1 (/ i n)) n) -100)
9.0ms	(pow (+ 1 (/ i n)) n)
13.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series1.1s

Counts

3 → 9

Calls

3 calls:

344.0ms	(fma 100 (pow (+ 1 (/ i n)) n) -100)
294.0ms	(pow (+ 1 (/ i n)) n)
454.0ms	(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1605
1	528
0	222

prune727.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.2b

localize18.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
5.6b	(log1p (/ i n))
10.2b	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
10.3b	(* n (log1p (/ i n)))

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:

0.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
1.0ms	(log1p (/ i n))
12.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
9.0ms	(* n (log1p (/ i n)))

series1.0s

Counts

4 → 12

Calls

4 calls:

331.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
58.0ms	(log1p (/ i n))
535.0ms	(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
86.0ms	(* n (log1p (/ i n)))

simplify2.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	2139
1	635
0	257

prune719.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.6b

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma 100 (exp (* n (log1p (/ i n)))) -100)
5.6b	(log1p (/ i n))
9.1b	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
10.3b	(* n (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-/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 100 (exp (* n (log1p (/ i n)))) -100)
0.0ms	(log1p (/ i n))
7.0ms	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
12.0ms	(* n (log1p (/ i n)))

series1.6s

Counts

4 → 12

Calls

4 calls:

288.0ms	(fma 100 (exp (* n (log1p (/ i n)))) -100)
73.0ms	(log1p (/ i n))
1.1s	(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
75.0ms	(* n (log1p (/ i n)))

simplify2.2s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1969
1	671
0	277

prune807.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1/100 n)
0.2b	(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
2.7b	(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
8.2b	(/ i (* n n))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

4.0ms	(/ 1/100 n)
4.0ms	(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
0.0ms	(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
7.0ms	(/ i (* n n))

series142.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1/100 n)
56.0ms	(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
43.0ms	(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
25.0ms	(/ i (* n n))

simplify1.8s

Counts

111 → 111

Iterations

Iter	Nodes
done	5003
3	2985
2	822
1	325
0	165

prune354.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.8b

regimes277.0ms

Accuracy

47.8% (10.4b remaining)

Error of 13.3b against oracle of 2.9b and baseline of 22.8b

bsearch239.0ms

Steps

Iters	Range		Point
9	2.784564170770455e-12	0.0004981816479932727	0.0004866774544189746
8	-0.5767180207385502	-5.6584428609239584e-05	-5.737712731949101e-05

simplify6.0ms

Iterations

Iter	Nodes
done	39
1	39
0	32

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.8s	2514×	body	1280	valid
2.4s	1006×	body	2560	valid
731.0ms	1632×	body	640	valid
271.0ms	845×	body	320	valid
228.0ms	3013×	body	80	valid
216.0ms	2294×	body	80	nan
68.0ms	440×	body	160	valid
33.0ms	8×	body	5120	valid