Details

sample252.0ms

Algorithm

intervals

Results

104.0ms	36×	body	2560	valid
87.0ms	77×	body	1280	valid
20.0ms	48×	body	640	valid
7.0ms	28×	body	320	valid
7.0ms	97×	body	80	valid
5.0ms	79×	body	80	nan
2.0ms	16×	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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize21.0ms

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)
5.6b	(pow (+ 1.0 (/ i n)) n)
12.6b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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:

437.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
203.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms	(pow (+ 1.0 (/ i n)) n)
433.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

564.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
349.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
324.0ms	(pow (+ 1.0 (/ i n)) n)
506.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify760.0ms

Counts

293 → 293

Iterations

Iter	Nodes
done	5001
1	1418
0	437

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0)
0.0b	(* (/ (* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0) i) n)
1.8b	(- (pow (+ (/ i n) 1.0) n) 1.0)
5.6b	(pow (+ (/ i n) 1.0) n)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`associate-l`
11×	`add-cube-cbrt`
9×	`pow1`
6×	`unpow-prod-down` `associate-r` `add-log-exp` `difference-of-squares`
5×	`prod-exp` `cbrt-unprod`
3×	`pow-unpow` `times-frac` `associate-*l/` `sqr-pow`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `pow-exp` `div-inv` `distribute-lft-out`

Counts

4 → 85

Calls

4 calls:

463.0ms	(* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0)
360.0ms	(* (/ (* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0) i) n)
171.0ms	(- (pow (+ (/ i n) 1.0) n) 1.0)
20.0ms	(pow (+ (/ i n) 1.0) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

285.0ms	(* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0)
406.0ms	(* (/ (* (- (pow (+ (/ i n) 1.0) n) 1.0) 100.0) i) n)
269.0ms	(- (pow (+ (/ i n) 1.0) n) 1.0)
232.0ms	(pow (+ (/ i n) 1.0) n)

simplify874.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2452
1	505
0	193

prune383.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0)
0.1b	(* (/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i) n)
11.5b	(/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i)
12.1b	(* (* i i) (log 1.0))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
11×	`associate-l`
10×	`associate-r`
9×	`prod-exp` `cbrt-unprod`
6×	`log-prod` `times-frac`
5×	`pow-prod-down` `associate-*l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`distribute-rgt-in` `associate-/r` `distribute-lft-in` `-commutative` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `log-pow` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

946.0ms	(* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0)
902.0ms	(* (/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i) n)
408.0ms	(/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i)
16.0ms	(* (* i i) (log 1.0))

series642.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0)
211.0ms	(* (/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i) n)
156.0ms	(/ (* (+ (- (+ (* (* i i) 0.5) (* 1.0 i)) (* 0.5 (* (* i i) (log 1.0)))) (* n (log 1.0))) 100.0) i)
161.0ms	(* (* i i) (log 1.0))

simplify1.6s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	3990
1	564
0	198

prune420.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.3b

localize35.0ms

Local error

Found 4 expressions with local error:

12.1b	(* (log 1.0) (- (* (* i i) 0.5) n))
15.0b	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
15.0b	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
15.0b	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 181

Calls

4 calls:

57.0ms	(* (log 1.0) (- (* (* i i) 0.5) n))
62.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
62.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
64.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))

series724.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (log 1.0) (- (* (* i i) 0.5) n))
203.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
210.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))
204.0ms	(/ (* (- (* i (+ 1.0 (* 0.5 i))) (* (log 1.0) (- (* (* i i) 0.5) n))) n) (/ i 100.0))

simplify1.3s

Counts

193 → 193

Iterations

Iter	Nodes
done	5000
2	4593
1	675
0	209

prune1.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

regimes244.0ms

Accuracy

59% (10.1b remaining)

Error of 19.0b against oracle of 8.9b and baseline of 33.6b

bsearch329.0ms

Steps

Iters	Range		Point
10	3.4680268680189636e-18	5.670292661026066e-06	5.5948792778141525e-06
3	2.1497245835393105e-249	3.176775141087436e-249	3.107272117925894e-249
11	-6.437211764621e+23	-2043.0247777912484	-2072.0844585672753

simplify19.0ms

Iterations

Iter	Nodes
done	70
1	70
0	54

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.0s	996×	body	2560	valid
1.9s	2494×	body	1280	valid
621.0ms	1640×	body	640	valid
372.0ms	2319×	body	80	nan
201.0ms	3016×	body	80	valid
185.0ms	851×	body	320	valid
50.0ms	435×	body	160	valid
34.0ms	3×	body	5120	valid