Details

sample288.0ms

Algorithm

intervals

Results

101.0ms	30×	body	2560	valid
100.0ms	79×	body	1280	valid
35.0ms	52×	body	640	valid
12.0ms	102×	body	80	valid
9.0ms	20×	body	320	valid
7.0ms	66×	body	80	nan
5.0ms	19×	body	160	valid
4.0ms	1×	body	5120	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	6722
5	1463
4	420
3	150
2	58
1	28
0	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.1b	(- (pow (+ 1 (/ i n)) n) 1)
7.3b	(pow (+ 1 (/ i n)) n)
8.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite464.0ms

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:

174.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
90.0ms	(- (pow (+ 1 (/ i n)) n) 1)
12.0ms	(pow (+ 1 (/ i n)) n)
170.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

388.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
282.0ms	(- (pow (+ 1 (/ i n)) n) 1)
268.0ms	(pow (+ 1 (/ i n)) n)
378.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.7s

Counts

465 → 465

Iterations

Iter	Nodes
2	5084
1	1658
0	542

prune4.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* i (* i i))
0.3b	(* 1/6 (* i (* i i)))
7.3b	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))
16.3b	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) (/ i n))

rewrite257.0ms

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:

14.0ms	(* i (* i i))
36.0ms	(* 1/6 (* i (* i i)))
40.0ms	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))
166.0ms	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) (/ i n))

series196.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* i (* i i))
42.0ms	(* 1/6 (* i (* i i)))
37.0ms	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))
71.0ms	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) (/ i n))

simplify606.0ms

Counts

146 → 146

Iterations

Iter	Nodes
2	2107
1	618
0	236

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 (* i (* i i)))
1.9b	(* (/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i) n)
4.7b	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i)
7.3b	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

32.0ms	(* 1/6 (* i (* i i)))
115.0ms	(* (/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i) n)
112.0ms	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i)
69.0ms	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/6 (* i (* i i)))
91.0ms	(* (/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i) n)
57.0ms	(/ (+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2))) i)
30.0ms	(+ (* 1/6 (* i (* i i))) (+ i (* (* i i) 1/2)))

simplify3.1s

Counts

111 → 111

Iterations

Iter	Nodes
3	7522
2	1530
1	436
0	165

prune993.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 i)
1.9b	(* (posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i))) n)
4.7b	(/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)
12.7b	(posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

9.0ms	(* 1/6 i)
10.0ms	(* (posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i))) n)
41.0ms	(/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)
0.0ms	(posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 1/6 i)
80.0ms	(* (posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i))) n)
56.0ms	(/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)
73.0ms	(posit16->real (real->posit16 (/ (+ i (* (* i i) (+ 1/2 (* 1/6 i)))) i)))

simplify1.3s

Counts

89 → 89

Iterations

Iter	Nodes
3	3986
2	924
1	294
0	128

prune2.0s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 10.5b

regimes729.0ms

Accuracy

54.3% (10.3b remaining)

Error of 20.7b against oracle of 10.3b and baseline of 32.9b

bsearch386.0ms

Steps

Iters	Range	Point
6	4.069861054943291e-182	3.002993785402301e-181	2.9484870312088923e-181
11	-1.0795694300690587e-07	-2.069612827053929e-28	-8.076739568312811e-20
8	-2.4422152478598623e+84	-8.368875907997448e+81	-1.8239091289757303e+82

Iters

Range

Point

4.069861054943291e-182

3.002993785402301e-181

2.9484870312088923e-181

-1.0795694300690587e-07

-2.069612827053929e-28

-8.076739568312811e-20

-2.4422152478598623e+84

-8.368875907997448e+81

-1.8239091289757303e+82

simplify10.0ms

Iterations

Iter	Nodes
2	41
1	41
0	32

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.1s	2555×	body	1280	valid
2.6s	989×	body	2560	valid
978.0ms	1582×	body	640	valid
703.0ms	848×	body	320	valid
368.0ms	3043×	body	80	valid
299.0ms	2348×	body	80	nan
106.0ms	460×	body	160	valid
31.0ms	6×	body	5120	valid