Details

sample408.0ms

Algorithm

intervals

Results

156.0ms	79×	body	1280	valid
144.0ms	38×	body	2560	valid
46.0ms	50×	body	640	valid
15.0ms	27×	body	320	valid
13.0ms	89×	body	80	valid
11.0ms	77×	body	80	nan
4.0ms	12×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5004
5	2473
4	512
3	150
2	58
1	28
0	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
2.7b	(- (pow (+ 1 (/ i n)) n) 1)
5.2b	(pow (+ 1 (/ i n)) n)
12.9b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite569.0ms

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)))
120.0ms	(- (pow (+ 1 (/ i n)) n) 1)
9.0ms	(pow (+ 1 (/ i n)) n)
228.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.5s

Counts

4 → 12

Calls

4 calls:

389.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
308.0ms	(- (pow (+ 1 (/ i n)) n) 1)
310.0ms	(pow (+ 1 (/ i n)) n)
456.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.8s

Counts

465 → 465

Iterations

Iter	Nodes
done	5001
1	1702
0	542

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.1b	(* 1/6 (* i (* i i)))
4.5b	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
18.2b	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
49×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `add-cube-cbrt`
27×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
6×	`associate-l`
5×	`pow-prod-up` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `sum-log` `div-exp` `associate-/l*`
2×	`flip3-+` `associate-r` `*-commutative` `flip-+` `associate-/l/`
1×	`pow2` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `associate-/r/` `pow-sqr` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

13.0ms	(* i (* i i))
34.0ms	(* 1/6 (* i (* i i)))
126.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
376.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

series235.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* i (* i i))
65.0ms	(* 1/6 (* i (* i i)))
34.0ms	(+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i))
72.0ms	(/ (+ (* (* 1/2 i) i) (+ (* 1/6 (* i (* i i))) i)) (/ i n))

simplify2.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5005
2	2329
1	627
0	238

prune620.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* i 1/6)
1.9b	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
2.6b	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
4.5b	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`associate-l`
13×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
8×	`pow1`
6×	`associate-r`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `pow-prod-down` `*-commutative` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `associate-*l/`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* i 1/6)
93.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
54.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
26.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* i 1/6)
65.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i)
88.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i))) i) n)
40.0ms	(+ (+ i (* (* i i) 1/2)) (* (* i 1/6) (* i i)))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5003
2	1536
1	409
0	156

prune500.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.2b

localize46.0ms

Local error

Found 4 expressions with local error:

1.9b	(/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i)
2.6b	(* (/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i) n)
4.5b	(+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i)))
60.0b	(posit16->real (real->posit16 (* i 1/6)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
9×	`add-log-exp`
6×	`pow1`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-/l`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative` `remove-posit16`

Counts

4 → 86

Calls

4 calls:

62.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i)
56.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i) n)
28.0ms	(+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i)))
0.0ms	(posit16->real (real->posit16 (* i 1/6)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i)
83.0ms	(* (/ (+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i))) i) n)
32.0ms	(+ (+ i (* (* i i) 1/2)) (* (posit16->real (real->posit16 (* i 1/6))) (* i i)))
17.0ms	(posit16->real (real->posit16 (* i 1/6)))

simplify1.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	5003
2	1313
1	361
0	144

prune641.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.2b

regimes260.0ms

Accuracy

57.1% (9.7b remaining)

Error of 19.6b against oracle of 10.0b and baseline of 32.5b

bsearch238.0ms

Steps

Iters	Range		Point
7	8.224021888767988e-168	2.0808644568757877e-166	5.351279663469521e-167
9	-489.75237388261763	-0.0005350557287305616	-1.1462618234168955

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	21

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.2s	2516×	body	1280	valid
2.5s	1021×	body	2560	valid
953.0ms	1583×	body	640	valid
636.0ms	2991×	body	80	valid
294.0ms	877×	body	320	valid
188.0ms	2267×	body	80	nan
82.0ms	386×	body	160	valid
22.0ms	5×	body	5120	valid