Details

sample210.0ms

Algorithm

intervals

Results

98.0ms	95×	body	1280	valid
54.0ms	22×	body	2560	valid
22.0ms	59×	body	640	valid
6.0ms	27×	body	320	valid
6.0ms	90×	body	80	valid
4.0ms	80×	body	80	nan
2.0ms	15×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	3444
5	877
4	318
3	139
2	60
1	25
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.0b	(pow (+ 1.0 (/ i n)) n)
9.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
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`

Counts

4 → 321

Calls

4 calls:

411.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
319.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms	(pow (+ 1.0 (/ i n)) n)
430.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

469.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
381.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
316.0ms	(pow (+ 1.0 (/ i n)) n)
554.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.4s

Counts

333 → 333

Iterations

Iter	Nodes
done	5000
1	1492
0	479

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
0.0b	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
10.4b	(* (* i i) (log 1.0))
15.8b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
85×	`*-un-lft-identity` `add-cube-cbrt`
48×	`associate-r`
23×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
12×	`pow1`
9×	`div-inv`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `log-pow` `fma-udef` `flip--`

Counts

4 → 181

Calls

4 calls:

0.0ms	(fma (* i i) 0.5 (* 1.0 i))
29.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
20.0ms	(* (* i i) (log 1.0))
40.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

series891.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma (* i i) 0.5 (* 1.0 i))
293.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
227.0ms	(* (* i i) (log 1.0))
264.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

simplify2.1s

Counts

193 → 193

Iterations

Iter	Nodes
done	5011
2	3495
1	966
0	324

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
1.8b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n))
10.4b	(* (* i i) (log 1.0))
11.1b	(* (/ 100.0 i) (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
120×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
91×	`add-cube-cbrt`
53×	`add-exp-log`
48×	`associate-r`
35×	`add-cbrt-cube`
23×	`div-exp`
14×	`associate-l`
13×	`associate-/r*` `prod-exp`
12×	`pow1` `cbrt-undiv`
10×	`div-inv`
9×	`cbrt-unprod` `unswap-sqr`
6×	`log-prod`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `flip3--` `div-sub` `associate-l/` `associate-r/` `log-pow` `fma-udef` `flip--`

Counts

4 → 210

Calls

4 calls:

0.0ms	(fma (* i i) 0.5 (* 1.0 i))
16.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n))
29.0ms	(* (* i i) (log 1.0))
77.0ms	(* (/ 100.0 i) (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n)))

series985.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma (* i i) 0.5 (* 1.0 i))
177.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n))
175.0ms	(* (* i i) (log 1.0))
562.0ms	(* (/ 100.0 i) (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 n)))

simplify2.2s

Counts

222 → 222

Iterations

Iter	Nodes
done	5070
2	3457
1	1175
0	362

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
0.0b	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
9.8b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
10.4b	(* (* i i) (log 1.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
17×	`pow1` `associate-l`
10×	`prod-exp` `cbrt-unprod`
8×	`associate-r`
7×	`pow-prod-down`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `cbrt-undiv` `associate-/r` `distribute-lft-in` `div-exp` `-commutative` `associate-/l*` `unswap-sqr`
2×	`associate-*l/` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

35.0ms	(* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
39.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
13.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
23.0ms	(* (* i i) (log 1.0))

series833.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n)
239.0ms	(* 100.0 (* (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i) n))
186.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
184.0ms	(* (* i i) (log 1.0))

simplify2.4s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1890
1	582
0	214

prune619.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 11.6b

regimes283.0ms

Accuracy

48.6% (11.4b remaining)

Error of 22.5b against oracle of 11.2b and baseline of 33.3b

bsearch244.0ms

Steps

Iters	Range		Point
7	4.3349714367632944e-150	5.208151982490766e-148	5.492513693153941e-150
6	-1.0692274826172779e-302	-7.189279918874739e-304	-2.7304039749009327e-303
7	-25254222.655854985	-733100.9210806559	-743560.0364592294

simplify11.0ms

Iterations

Iter	Nodes
done	55
1	55
0	43

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.1s	2501×	body	1280	valid
2.0s	947×	body	2560	valid
564.0ms	1605×	body	640	valid
558.0ms	854×	body	320	valid
231.0ms	3080×	body	80	valid
121.0ms	443×	body	160	valid
95.0ms	2179×	body	80	nan
45.0ms	9×	body	5120	valid