Details

sample256.0ms

Algorithm

intervals

Results

114.0ms	39×	body	2560	valid
71.0ms	76×	body	1280	valid
31.0ms	61×	body	640	valid
7.0ms	27×	body	320	valid
6.0ms	90×	body	80	valid
4.0ms	64×	body	80	nan
2.0ms	12×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1535
4	347
3	140
2	59
1	25
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.1b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite983.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
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` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

421.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
171.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms	(pow (+ 1.0 (/ i n)) n)
352.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

529.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
343.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
252.0ms	(pow (+ 1.0 (/ i n)) n)
503.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.2s

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* i i) 0.5) (* 1.0 i))
0.1b	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
10.9b	(* (log 1.0) (* (* i i) 0.5))
18.8b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite581.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
151×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
97×	`add-cube-cbrt`
58×	`associate-r`
27×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
16×	`pow1`
13×	`associate-/r*`
11×	`div-inv`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-l` `pow-prod-down`
6×	`cbrt-undiv` `div-exp` `add-log-exp` `associate-/l/`
4×	`flip3-+` `frac-add` `flip-+` `associate-/l*`
3×	`unswap-sqr`
2×	`flip3--` `associate-/r/` `*-commutative` `flip--`
1×	`+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-sub` `associate-*r/` `log-pow`

Counts

4 → 203

Calls

4 calls:

14.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
282.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
37.0ms	(* (log 1.0) (* (* i i) 0.5))
236.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series826.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
267.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
197.0ms	(* (log 1.0) (* (* i i) 0.5))
260.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify1.7s

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1064
0	336

prune1.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(- n (* i (* i 0.5)))
0.1b	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) n))
10.2b	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
10.9b	(* (log 1.0) (- n (* i (* i 0.5))))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1`
9×	`times-frac`
7×	`associate-l`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`associate-r` `pow-prod-down`
3×	`associate-/r` `sub-neg` `associate-r/` `associate-/l*`
2×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `flip3--` `div-exp` `*-commutative` `flip--` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3-+` `diff-log` `associate-*l/` `log-pow` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

4.0ms	(- n (* i (* i 0.5)))
108.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) n))
110.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
21.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- n (* i (* i 0.5)))
249.0ms	(* 100.0 (* (/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i) n))
147.0ms	(/ (+ (+ (* (log 1.0) (- n (* i (* i 0.5)))) (* i (* i 0.5))) (* 1.0 i)) i)
218.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify1.8s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2612
1	482
0	180

prune629.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 11.5b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* i i) 0.5) (* 1.0 i))
2.3b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
10.9b	(* (log 1.0) (* (* i i) 0.5))
11.9b	(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

rewrite623.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
159×	`*-un-lft-identity`
131×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
58×	`associate-r`
57×	`add-exp-log`
39×	`add-cbrt-cube`
27×	`distribute-lft-out`
23×	`div-exp`
17×	`associate-l`
16×	`pow1` `prod-exp`
13×	`associate-/r*`
12×	`cbrt-undiv` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
7×	`pow-prod-down`
6×	`add-log-exp` `associate-/l/`
4×	`flip3-+` `frac-add` `flip-+` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`flip3--` `associate-/r/` `*-commutative` `flip--`
1×	`frac-times` `+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-sub` `associate-l/` `associate-r/` `log-pow`

Counts

4 → 232

Calls

4 calls:

14.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
265.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
37.0ms	(* (log 1.0) (* (* i i) 0.5))
297.0ms	(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
189.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n))
247.0ms	(* (log 1.0) (* (* i i) 0.5))
267.0ms	(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ 1 n)))

simplify1.3s

Counts

244 → 244

Iterations

Iter	Nodes
done	5001
1	1289
0	375

prune1.2s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.5b

regimes392.0ms

Accuracy

53.5% (10.7b remaining)

Error of 21.7b against oracle of 11.1b and baseline of 34.0b

bsearch398.0ms

Steps

Iters	Range		Point
9	7.674138475383248	1698412.1750747235	7.743283777926976
10	-3.124575090294561e-11	-2.0990955826697636e-21	-3.0764933618318215e-11

simplify37.0ms

Iterations

Iter	Nodes
done	60
1	60
0	43

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.8s	2448×	body	1280	valid
2.6s	967×	body	2560	valid
895.0ms	1652×	body	640	valid
623.0ms	3015×	body	80	valid
220.0ms	867×	body	320	valid
150.0ms	2204×	body	80	nan
65.0ms	409×	body	160	valid
47.0ms	10×	body	5120	valid