Details

sample345.0ms

Algorithm

intervals

Results

128.0ms	34×	body	2560	valid
127.0ms	77×	body	1280	valid
35.0ms	48×	body	640	valid
15.0ms	113×	body	80	valid
12.0ms	24×	body	320	valid
9.0ms	70×	body	80	nan
3.0ms	11×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
5	2006
4	512
3	150
2	58
1	28
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
7.1b	(pow (+ 1 (/ i n)) n)
9.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite526.0ms

Algorithm

rewrite-expression-head

Rules

584×	`times-frac`
485×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
224×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
29×	`div-inv`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r` `associate-/l`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`insert-posit16`
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 → 453

Calls

4 calls:

192.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
91.0ms	(- (pow (+ 1 (/ i n)) n) 1)
16.0ms	(pow (+ 1 (/ i n)) n)
215.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
324.0ms	(- (pow (+ 1 (/ i n)) n) 1)
259.0ms	(pow (+ 1 (/ i n)) n)
332.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.4s

Counts

465 → 465

Iterations

Iter	Nodes
done	2001
2	2001
1	1702
0	542

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
1.2b	(- (pow (+ 1 (/ i n)) n) 1)
3.5b	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))
7.1b	(pow (+ 1 (/ i n)) n)

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

997×	`times-frac`
503×	`add-sqr-sqrt`
409×	`*-un-lft-identity`
287×	`add-cube-cbrt`
165×	`cbrt-prod`
144×	`difference-of-squares`
76×	`unpow-prod-down`
73×	`sqr-pow`
72×	`difference-of-sqr-1`
42×	`div-inv`
26×	`add-exp-log`
24×	`distribute-lft-out--`
22×	`associate-/r*`
18×	`add-cbrt-cube`
17×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`insert-posit16`
3×	`pow-unpow`
2×	`div-sub` `prod-exp` `cbrt-unprod`
1×	`pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `flip3--` `pow1/3` `diff-log` `pow-exp` `associate-/r/` `flip--` `distribute-lft-out` `associate-/l/`

Counts

4 → 493

Calls

4 calls:

1.0ms	(cbrt i)
107.0ms	(- (pow (+ 1 (/ i n)) n) 1)
203.0ms	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))
16.0ms	(pow (+ 1 (/ i n)) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

228.0ms	(cbrt i)
268.0ms	(- (pow (+ 1 (/ i n)) n) 1)
467.0ms	(/ (/ (- (pow (+ 1 (/ i n)) n) 1) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))
339.0ms	(pow (+ 1 (/ i n)) n)

simplify1.2s

Counts

505 → 505

Iterations

Iter	Nodes
done	2000
1	2000
0	724

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
1.8b	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i)))
5.5b	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
9.1b	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
157×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
75×	`cbrt-prod`
33×	`div-inv`
30×	`add-exp-log`
23×	`associate-/r*`
21×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
10×	`associate-/l*`
9×	`add-log-exp`
4×	`pow1` `insert-posit16`
3×	`sum-log` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `pow1/3` `associate-/r/`

Counts

4 → 258

Calls

4 calls:

1.0ms	(cbrt i)
131.0ms	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i)))
32.0ms	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
77.0ms	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))

series485.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt i)
123.0ms	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i)))
32.0ms	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
117.0ms	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (* (cbrt i) (cbrt i))) (/ (cbrt i) n))

simplify1.3s

Counts

270 → 270

Iterations

Iter	Nodes
done	2018
2	2018
1	1613
0	466

prune1.5s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i))
2.8b	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n))
5.5b	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
8.9b	(* (/ (/ 1 (cbrt i)) (cbrt i)) (/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

2153×	`times-frac`
1395×	`add-sqr-sqrt`
885×	`*-un-lft-identity`
809×	`add-cube-cbrt`
501×	`cbrt-prod`
291×	`associate-r`
233×	`add-exp-log`
151×	`div-exp`
136×	`associate-l`
120×	`unswap-sqr`
92×	`div-inv`
63×	`add-cbrt-cube`
48×	`cbrt-undiv`
45×	`prod-exp`
25×	`associate-/l*`
21×	`rec-exp` `1-exp`
19×	`associate-/r*`
15×	`cbrt-unprod`
9×	`add-log-exp`
6×	`pow1`
4×	`insert-posit16`
3×	`sum-log` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-/r/` `flip-+`
1×	`frac-times` `+-commutative` `associate-+l+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 1022

Calls

4 calls:

106.0ms	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i))
102.0ms	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n))
33.0ms	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
100.0ms	(* (/ (/ 1 (cbrt i)) (cbrt i)) (/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i))
194.0ms	(/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n))
41.0ms	(+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i))))
102.0ms	(* (/ (/ 1 (cbrt i)) (cbrt i)) (/ (/ (+ (+ i (* 1/2 (* i i))) (* 1/6 (* i (* i i)))) (cbrt i)) (/ 1 n)))

simplify1.7s

Counts

1034 → 1034

Iterations

Iter	Nodes
done	2000
1	2000
0	1260

prune5.1s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 8.1b

regimes616.0ms

Accuracy

55.1% (10.2b remaining)

Error of 20.8b against oracle of 10.5b and baseline of 33.3b

bsearch215.0ms

Steps

Iters	Range		Point
8	2.5250088521112566e-199	6.797742076970442e-197	5.021135972250703e-197
11	-1.2475612113013005e+20	-0.005838610583870787	-1.3019374668740835

simplify4.0ms

Iterations

Iter	Nodes
done	30
1	30
0	20

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.2s	2493×	body	1280	valid
2.5s	973×	body	2560	valid
1.3s	1635×	body	640	valid
398.0ms	831×	body	320	valid
363.0ms	3042×	body	80	valid
218.0ms	2287×	body	80	nan
132.0ms	477×	body	160	valid
44.0ms	10×	body	5120	valid