Details

sample303.0ms

Algorithm

intervals

Results

117.0ms	40×	body	2560	valid
102.0ms	76×	body	1280	valid
32.0ms	53×	body	640	valid
11.0ms	91×	body	80	valid
10.0ms	22×	body	320	valid
9.0ms	74×	body	80	nan
3.0ms	12×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.0b	(- (pow (+ 1 (/ i n)) n) 1)
6.0b	(pow (+ 1 (/ i n)) n)
13.2b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite549.0ms

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:

208.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
140.0ms	(- (pow (+ 1 (/ i n)) n) 1)
11.0ms	(pow (+ 1 (/ i n)) n)
178.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

354.0ms	(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
270.0ms	(- (pow (+ 1 (/ i n)) n) 1)
250.0ms	(pow (+ 1 (/ i n)) n)
395.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify8.4s

Counts

465 → 465

Iterations

Iter	Nodes
2	5274
1	1671
0	542

prune4.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
0.5b	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
1.0b	(- (pow (+ 1 (/ i n)) n) 1)
6.0b	(pow (+ 1 (/ i n)) n)

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

604×	`times-frac`
510×	`add-sqr-sqrt`
374×	`*-un-lft-identity`
230×	`add-cube-cbrt`
174×	`associate-r`
168×	`difference-of-squares`
88×	`unpow-prod-down`
85×	`sqr-pow`
84×	`difference-of-sqr-1`
49×	`add-exp-log`
30×	`add-cbrt-cube` `div-inv`
28×	`distribute-lft-out--`
23×	`div-exp`
13×	`associate-/r` `associate-l` `associate-/l`
12×	`cbrt-undiv`
10×	`prod-exp`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`rec-exp` `pow-unpow` `1-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`frac-times` `pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `pow-exp` `associate-r/` `*-commutative` `distribute-lft-out`

Counts

4 → 482

Calls

4 calls:

216.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
230.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
133.0ms	(- (pow (+ 1 (/ i n)) n) 1)
16.0ms	(pow (+ 1 (/ i n)) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

328.0ms	(/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n))
362.0ms	(* (/ 100 i) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ 1 n)))
308.0ms	(- (pow (+ 1 (/ i n)) n) 1)
294.0ms	(pow (+ 1 (/ i n)) n)

simplify28.4s

Counts

494 → 494

Iterations

Iter	Nodes
2	4873
1	1958
0	565

prune3.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* i (* i i)) 1/6)
1.8b	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
7.0b	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
10.8b	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
159×	`*-un-lft-identity`
131×	`add-sqr-sqrt`
103×	`add-cube-cbrt`
60×	`associate-r`
57×	`add-exp-log`
39×	`add-cbrt-cube`
27×	`distribute-lft-out`
23×	`div-exp`
16×	`prod-exp`
15×	`pow1`
14×	`associate-l`
13×	`associate-/r*`
12×	`cbrt-undiv` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
7×	`pow-prod-down`
6×	`add-log-exp`
4×	`insert-posit16` `associate-/l*`
3×	`rec-exp` `1-exp`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 230

Calls

4 calls:

40.0ms	(* (* i (* i i)) 1/6)
166.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
17.0ms	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
172.0ms	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* i (* i i)) 1/6)
47.0ms	(/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n))
97.0ms	(+ (* (* i i) 1/2) (* (* i (* i i)) 1/6))
70.0ms	(* (/ 100 i) (/ (+ (+ (* (* i i) 1/2) (* (* i (* i i)) 1/6)) i) (/ 1 n)))

simplify2.8s

Counts

242 → 242

Iterations

Iter	Nodes
2	3748
1	1098
0	347

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.5b

localize54.0ms

Local error

Found 4 expressions with local error:

1.7b	(* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)
3.5b	(* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n))
6.9b	(* (/ (* (cbrt 100) (cbrt 100)) (* (cbrt i) (cbrt i))) (* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)))
7.0b	(+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2))

rewrite412.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-exp-log`
84×	`add-cbrt-cube`
82×	`prod-exp` `cbrt-unprod`
48×	`associate-l`
37×	`times-frac`
36×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
20×	`pow1`
18×	`associate-*l/`
11×	`frac-times` `associate-*r/`
10×	`pow-prod-down`
9×	`add-log-exp`
8×	`flip3-+` `flip-+`
5×	`associate-r`
4×	`insert-posit16`
3×	`sum-log` `*-commutative`
2×	`div-inv`
1×	`+-commutative` `associate-+l+` `unswap-sqr`

Counts

4 → 179

Calls

4 calls:

55.0ms	(* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)
81.0ms	(* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n))
247.0ms	(* (/ (* (cbrt 100) (cbrt 100)) (* (cbrt i) (cbrt i))) (* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)))
26.0ms	(+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2))

series438.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)
196.0ms	(* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n))
166.0ms	(* (/ (* (cbrt 100) (cbrt 100)) (* (cbrt i) (cbrt i))) (* (/ (cbrt 100) (cbrt i)) (* (+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2)) n)))
27.0ms	(+ (+ i (* i (* i (* i 1/6)))) (* (* i i) 1/2))

simplify1.4s

Counts

191 → 191

Iterations

Iter	Nodes
2	4960
1	952
0	303

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.4b

regimes265.0ms

Accuracy

52% (10.8b remaining)

Error of 22.0b against oracle of 11.2b and baseline of 33.7b

bsearch540.0ms

Steps

Iters	Range		Point
11	1.4748909779041237	1.2739090897902979e+25	3.902656912278071
10	-1.6659712673405804e-287	-7.121156334981362e-300	-1.8925394344879332e-295
2	-1.3545439389701445e+37	-1.1399582415865866e+37	-1.1667814537595314e+37

simplify9.0ms

Iterations

Iter	Nodes
2	58
1	58
0	43

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2393×	body	1280	valid
2.1s	999×	body	2560	valid
812.0ms	1595×	body	640	valid
327.0ms	441×	body	160	valid
316.0ms	3078×	body	80	valid
269.0ms	892×	body	320	valid
180.0ms	2350×	body	80	nan
24.0ms	7×	body	5120	valid