Details

sample243.0ms

Algorithm

intervals

Results

93.0ms	39×	body	2560	valid
72.0ms	75×	body	1280	valid
20.0ms	71×	body	80	nan
19.0ms	47×	body	640	valid
7.0ms	105×	body	80	valid
6.0ms	20×	body	320	valid
3.0ms	20×	body	160	valid

simplify6.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
6	3302
5	836
4	309
3	135
2	59
1	25
0	10

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.9b	(pow (+ 1.0 (/ i n)) n)
12.6b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.7s

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`
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 → 285

Calls

4 calls:

673.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
342.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
599.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.4s

Counts

4 → 12

Calls

4 calls:

841.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
488.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
412.0ms	(pow (+ 1.0 (/ i n)) n)
682.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify4.8s

Counts

297 → 297

Iterations

Iter	Nodes
done	5001
2	4691
1	1394
0	441

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n)))
10.4b	(* (* (* i i) 0.5) (log 1.0))
21.2b	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
96×	`add-sqr-sqrt`
86×	`*-un-lft-identity` `add-cube-cbrt`
51×	`associate-r`
32×	`add-cbrt-cube` `add-exp-log`
21×	`pow1`
13×	`associate-/r*`
12×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
9×	`div-inv`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`associate-/r/` `associate-/l/`
1×	`clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `log-pow` `flip-+`

Counts

4 → 190

Calls

4 calls:

23.0ms	(* (* i i) 0.5)
247.0ms	(* 100.0 (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n)))
76.0ms	(* (* (* i i) 0.5) (log 1.0))
268.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n))

series718.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* i i) 0.5)
265.0ms	(* 100.0 (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n)))
183.0ms	(* (* (* i i) 0.5) (log 1.0))
234.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) (/ i n))

simplify4.1s

Counts

202 → 202

Iterations

Iter	Nodes
done	5003
2	3659
1	966
0	337

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* i i) 0.5)
0.1b	(* 100.0 (* (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i) n))
9.9b	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
10.4b	(* (* (* i i) 0.5) (log 1.0))

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-cbrt-cube` `add-exp-log`
24×	`pow1`
18×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`times-frac`
8×	`associate-r`
6×	`log-prod`
5×	`associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-/l/`
1×	`clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `associate-l/` `associate-r/` `log-pow` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

24.0ms	(* (* i i) 0.5)
191.0ms	(* 100.0 (* (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i) n))
263.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
79.0ms	(* (* (* i i) 0.5) (log 1.0))

series674.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* i i) 0.5)
261.0ms	(* 100.0 (* (/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i) n))
191.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
191.0ms	(* (* (* i i) 0.5) (log 1.0))

simplify2.7s

Counts

114 → 114

Iterations

Iter	Nodes
done	5004
2	1942
1	534
0	205

prune961.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.3b

localize158.0ms

Local error

Found 4 expressions with local error:

9.9b	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
10.4b	(* (* (* i i) 0.5) (log 1.0))
10.4b	(* (* (* i i) 0.5) (log 1.0))
10.4b	(* (* (* i i) 0.5) (log 1.0))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
33×	`add-cbrt-cube` `add-exp-log`
21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-r`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-l` `log-pow` `-commutative` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `associate-+r-` `frac-2neg` `flip3-+` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 118

Calls

4 calls:

261.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
75.0ms	(* (* (* i i) 0.5) (log 1.0))
75.0ms	(* (* (* i i) 0.5) (log 1.0))
76.0ms	(* (* (* i i) 0.5) (log 1.0))

series756.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ (+ (* n (log 1.0)) (- (+ (* 1.0 i) (* (* i i) 0.5)) (* (* (* i i) 0.5) (log 1.0)))) i)
186.0ms	(* (* (* i i) 0.5) (log 1.0))
189.0ms	(* (* (* i i) 0.5) (log 1.0))
188.0ms	(* (* (* i i) 0.5) (log 1.0))

simplify2.0s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1246
1	357
0	138

prune1.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.3b

regimes800.0ms

Accuracy

50.3% (11.4b remaining)

Error of 22.0b against oracle of 10.6b and baseline of 33.6b

bsearch694.0ms

Steps

Iters	Range		Point
7	4.844052074247226e-103	1.4804481956603392e-101	4.930404890743995e-103
7	-1.903881763283314e-306	-7.036936607564605e-308	-3.388139377181462e-307
10	-524937.0299516014	-3.8822111449762154e-05	-2.4617384878412216
9	-6.999589544614527e+61	-8.353436009901676e+53	-3.0859985436646373e+59
9	-2.4334994185842963e+101	-8.921734026293468e+92	-1.4968988971170808e+97

simplify34.0ms

Iterations

Iter	Nodes
done	70
1	70
0	53

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.1s	2496×	body	1280	valid
1.9s	999×	body	2560	valid
622.0ms	1571×	body	640	valid
456.0ms	3075×	body	80	valid
194.0ms	859×	body	320	valid
86.0ms	2226×	body	80	nan
77.0ms	417×	body	160	valid
27.0ms	7×	body	5120	valid