Details

sample312.0ms

Algorithm

intervals

Results

120.0ms	80×	body	1280	valid
101.0ms	27×	body	2560	valid
32.0ms	52×	body	640	valid
11.0ms	31×	body	320	valid
9.0ms	86×	body	80	valid
6.0ms	71×	body	80	nan
3.0ms	15×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1593
4	364
3	144
2	60
1	25
0	10

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `associate-r/` `-commutative`

Counts

4 → 321

Calls

4 calls:

458.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
224.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
414.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts

4 → 12

Calls

4 calls:

599.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
340.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
294.0ms	(pow (+ 1.0 (/ i n)) n)
656.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify884.0ms

Counts

333 → 333

Iterations

Iter	Nodes
done	5001
1	1521
0	479

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
0.1b	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
10.6b	(* (* 0.5 (log 1.0)) (* i i))
16.6b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
91×	`add-sqr-sqrt`
82×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-r`
30×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
13×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `fma-udef` `flip--`

Counts

4 → 177

Calls

4 calls:

0.0ms	(fma (* i i) 0.5 (* 1.0 i))
30.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
48.0ms	(* (* 0.5 (log 1.0)) (* i i))
19.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (* i i) 0.5 (* 1.0 i))
608.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
213.0ms	(* (* 0.5 (log 1.0)) (* i i))
235.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

simplify493.0ms

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	972
0	314

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
2.6b	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
10.6b	(* (* (* i i) 0.5) (log 1.0))
12.9b	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log`
45×	`add-cbrt-cube`
40×	`prod-exp`
30×	`pow1`
24×	`cbrt-unprod`
20×	`associate-l`
19×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`pow-prod-down`
12×	`associate-*l/`
9×	`times-frac` `associate-r` `associate-*r/`
8×	`div-exp`
6×	`log-prod`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `cbrt-undiv` `rec-exp` `1-exp` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
1×	`log-pow` `div-inv` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

72.0ms	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
15.0ms	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
47.0ms	(* (* (* i i) 0.5) (log 1.0))
37.0ms	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

series774.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* 100.0 (* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)))
155.0ms	(* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n)
185.0ms	(* (* (* i i) 0.5) (log 1.0))
208.0ms	(* (/ 1 i) (* (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))) n))

simplify355.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
1	761
0	253

prune633.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
0.1b	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
10.1b	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
10.6b	(* (* (* i i) 0.5) (log 1.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube` `add-exp-log`
19×	`times-frac`
18×	`pow1`
17×	`associate-l`
11×	`associate-r`
9×	`prod-exp` `cbrt-unprod`
8×	`pow-prod-down`
6×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
5×	`associate-*l/`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `div-exp` `prod-diff` `div-inv`
1×	`clear-num` `frac-2neg` `flip3--` `distribute-rgt-out--` `log-pow` `frac-sub` `flip--` `sub-div`

Counts

4 → 124

Calls

4 calls:

13.0ms	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
34.0ms	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
6.0ms	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
47.0ms	(* (* (* i i) 0.5) (log 1.0))

series568.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
188.0ms	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
87.0ms	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
182.0ms	(* (* (* i i) 0.5) (log 1.0))

simplify1.6s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	3710
1	644
0	246

prune571.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 10.7b

regimes330.0ms

Accuracy

55.9% (9.3b remaining)

Error of 20.5b against oracle of 11.2b and baseline of 32.3b

bsearch442.0ms

Steps

Iters	Range		Point
9	1.163556109256494e+295	1.214614523789834e+300	1.844738975002478e+296
10	3.342414265731644e+225	5.061750323853299e+237	8.608246042115979e+235
9	3.955388158466523e-19	1.5375988180684124e-09	1.5086524363033694e-09
9	-346749.28651926527	-0.4133142809703875	-0.9893212200252494

simplify11.0ms

Iterations

Iter	Nodes
done	85
2	85
1	83
0	65

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	2642×	body	1280	valid
1.7s	887×	body	2560	valid
532.0ms	1648×	body	640	valid
189.0ms	864×	body	320	valid
180.0ms	2969×	body	80	valid
147.0ms	2291×	body	80	nan
55.0ms	450×	body	160	valid
29.0ms	8×	body	5120	valid