Details

sample232.0ms

Algorithm

intervals

Results

90.0ms	80×	body	1280	valid
73.0ms	27×	body	2560	valid
23.0ms	52×	body	640	valid
8.0ms	31×	body	320	valid
6.0ms	86×	body	80	valid
4.0ms	71×	body	80	nan
2.0ms	15×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.2b

localize19.0ms

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))

rewrite985.0ms

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:

410.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
158.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms	(pow (+ 1.0 (/ i n)) n)
368.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

476.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
325.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
562.0ms	(pow (+ 1.0 (/ i n)) n)
439.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify704.0ms

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.7b

localize26.0ms

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)))
10.6b	(* (log 1.0) (* (* i i) 0.5))
16.6b	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

rewrite591.0ms

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:

15.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
278.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
47.0ms	(* (log 1.0) (* (* i i) 0.5))
241.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

series788.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (* (* i i) 0.5) (* 1.0 i))
274.0ms	(* 100.0 (/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n)))
210.0ms	(* (log 1.0) (* (* i i) 0.5))
221.0ms	(/ (+ (+ (* (* i i) 0.5) (* 1.0 i)) (- (* n (log 1.0)) (* (log 1.0) (* (* i i) 0.5)))) (/ i n))

simplify409.0ms

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1064
0	336

prune989.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.7b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

67×	`associate-*r/`
62×	`add-exp-log`
38×	`add-cbrt-cube`
35×	`prod-exp`
32×	`associate-*l/`
23×	`pow1` `associate-l`
20×	`add-sqr-sqrt` `frac-add`
19×	`cbrt-unprod`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`flip3-+` `flip-+`
12×	`frac-times`
11×	`flip3--` `pow-prod-down` `flip--`
9×	`times-frac`
8×	`div-exp` `associate-r`
4×	`cbrt-undiv` `rec-exp` `1-exp` `*-commutative` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `unswap-sqr`
1×	`log-pow` `div-inv`

Counts

4 → 140

Calls

4 calls:

178.0ms	(* 100.0 (* (/ 1 i) (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n)))
41.0ms	(* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n)
14.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
77.0ms	(* (/ 1 i) (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n))

series750.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* 100.0 (* (/ 1 i) (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n)))
146.0ms	(* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n)
177.0ms	(* (log 1.0) (- n (* i (* i 0.5))))
200.0ms	(* (/ 1 i) (* (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) n))

simplify355.0ms

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
1	951
0	287

prune825.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 10.7b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

20.0ms	(* i (+ (* i 0.5) 1.0))
43.0ms	(* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) i) (* n 100.0))
41.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) i)
14.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* i (+ (* i 0.5) 1.0))
217.0ms	(* (/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) i) (* n 100.0))
143.0ms	(/ (+ (* i (+ (* i 0.5) 1.0)) (* (log 1.0) (- n (* i (* i 0.5))))) i)
173.0ms	(* (log 1.0) (- n (* i (* i 0.5))))

simplify1.3s

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
2	4025
1	696
0	224

prune541.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 10.7b

regimes365.0ms

Accuracy

55.8% (9.4b remaining)

Error of 20.5b against oracle of 11.1b and baseline of 32.3b

bsearch430.0ms

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

simplify9.0ms

Iterations

Iter	Nodes
done	81
1	81
0	58

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.6s	2642×	body	1280	valid
1.8s	887×	body	2560	valid
586.0ms	1648×	body	640	valid
163.0ms	864×	body	320	valid
153.0ms	2969×	body	80	valid
119.0ms	2291×	body	80	nan
83.0ms	450×	body	160	valid
29.0ms	8×	body	5120	valid