Details

sample293.0ms

Algorithm

intervals

Results

111.0ms	86×	body	1280	valid
79.0ms	25×	body	2560	valid
36.0ms	52×	body	640	valid
26.0ms	76×	body	80	nan
12.0ms	101×	body	80	valid
9.0ms	23×	body	320	valid
5.0ms	18×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
6	7318
5	1480
4	419
3	148
2	56
1	26
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
2.0b	(- (pow (+ 1 (/ i n)) n) 1)
5.6b	(pow (+ 1 (/ i n)) n)
8.0b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite479.0ms

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:

188.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
79.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
191.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.6s

Counts

4 → 12

Calls

4 calls:

504.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
324.0ms	(- (pow (+ 1 (/ i n)) n) 1)
308.0ms	(pow (+ 1 (/ i n)) n)
417.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify8.9s

Counts

465 → 465

Iterations

Iter	Nodes
2	5274
1	1671
0	542

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 1/6 (* i i)) i)
0.4b	(* 1/6 (* i i))
6.5b	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
14.4b	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

97×	`times-frac`
83×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
55×	`add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
14×	`distribute-lft-out`
13×	`associate-/r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`div-inv` `add-log-exp`
4×	`associate-r` `associate-l` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`flip3-+` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-/r/` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

38.0ms	(* (* 1/6 (* i i)) i)
14.0ms	(* 1/6 (* i i))
16.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
165.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

series248.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 1/6 (* i i)) i)
32.0ms	(* 1/6 (* i i))
105.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))
71.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) (/ i n))

simplify1000.0ms

Counts

153 → 153

Iterations

Iter	Nodes
2	2493
1	657
0	237

prune490.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/6 (* i i))
2.1b	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
4.2b	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
6.5b	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
19×	`associate-l`
16×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
7×	`distribute-lft-out`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down` `insert-posit16` `associate-/l*`
3×	`associate-/r*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `*-commutative` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-*l/`

Counts

4 → 102

Calls

4 calls:

14.0ms	(* 1/6 (* i i))
172.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
158.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
21.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

series248.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 (* i i))
70.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i) n)
46.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i)) i) i)
105.0ms	(+ (* (* i i) 1/2) (* (* 1/6 (* i i)) i))

simplify4.0s

Counts

114 → 114

Iterations

Iter	Nodes
3	7657
2	1574
1	450
0	163

prune384.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 1/6)
2.1b	(* (/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i) n)
4.2b	(/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i)
6.5b	(+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
16×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out`
6×	`pow1` `add-log-exp`
4×	`insert-posit16` `associate-/l*`
3×	`cbrt-prod` `associate-/r` `associate-r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow1/3` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 94

Calls

4 calls:

1.0ms	(cbrt 1/6)
238.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i) n)
220.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i)
24.0ms	(+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i))

series431.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 1/6)
111.0ms	(* (/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i) n)
93.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i)) i) i)
227.0ms	(+ (* (* i i) 1/2) (* (* (* (cbrt 1/6) (cbrt 1/6)) (* (cbrt 1/6) (* i i))) i))

simplify2.9s

Counts

104 → 104

Iterations

Iter	Nodes
3	7333
2	1442
1	397
0	151

prune289.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

regimes204.0ms

Accuracy

54.3% (10.5b remaining)

Error of 21.3b against oracle of 10.9b and baseline of 33.8b

bsearch350.0ms

Steps

Iters	Range		Point
11	2.9348777329819658e-12	3.1891227468784625e+20	4.5457902375689345
9	-1.9696345359431407e-07	-4.750217372511675e-17	-1.9324505473046543e-07

simplify12.0ms

Iterations

Iter	Nodes
2	49
1	49
0	38

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.4s	2440×	body	1280	valid
2.1s	957×	body	2560	valid
1.1s	1643×	body	640	valid
285.0ms	877×	body	320	valid
256.0ms	3092×	body	80	valid
193.0ms	2249×	body	80	nan
113.0ms	445×	body	160	valid
25.0ms	6×	body	5120	valid