Details

sample269.0ms

Algorithm

intervals

Results

106.0ms	89×	body	1280	valid
90.0ms	35×	body	2560	valid
24.0ms	46×	body	640	valid
15.0ms	86×	body	80	valid
9.0ms	33×	body	320	valid
4.0ms	73×	body	80	nan
1.0ms	7×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1593
4	364
3	144
2	60
1	25
0	10

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 45.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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:

431.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
289.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
388.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

487.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
344.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
343.0ms	(pow (+ 1.0 (/ i n)) n)
585.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify932.0ms

Counts

333 → 333

Iterations

Iter	Nodes
done	5001
1	1521
0	479

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* i i) 0.5 (* 1.0 i))
0.1b	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
8.2b	(* (* 0.5 (log 1.0)) (* i i))
18.8b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
91×	`add-sqr-sqrt`
82×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-r`
30×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
13×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `unswap-sqr`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*r/` `fma-udef` `flip--`

Counts

4 → 177

Calls

4 calls:

0.0ms	(fma (* i i) 0.5 (* 1.0 i))
58.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
38.0ms	(* (* 0.5 (log 1.0)) (* i i))
23.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

series887.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma (* i i) 0.5 (* 1.0 i))
297.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n)))
255.0ms	(* (* 0.5 (log 1.0)) (* i i))
246.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* 0.5 (log 1.0)) (* i i))) (/ i n))

simplify971.0ms

Counts

189 → 189

Iterations

Iter	Nodes
done	5001
1	972
0	314

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
0.1b	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
7.7b	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
8.2b	(* (* (* i i) 0.5) (log 1.0))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

25.0ms	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
45.0ms	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
6.0ms	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
90.0ms	(* (* (* i i) 0.5) (log 1.0))

series734.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n)
256.0ms	(* 100.0 (- (* (/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i) n) (* (/ (* (* (* i i) 0.5) (log 1.0)) i) n)))
105.0ms	(/ (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) i)
258.0ms	(* (* (* i i) 0.5) (log 1.0))

simplify2.4s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	3710
1	644
0	246

prune990.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.7b

localize113.0ms

Local error

Found 4 expressions with local error:

8.2b	(* (* (* i i) 0.5) (log 1.0))
8.4b	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
8.4b	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
8.4b	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod`
6×	`cbrt-div` `log-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `pow1/3` `flip--`
1×	`associate-l` `log-pow` `*-commutative`

Counts

4 → 75

Calls

4 calls:

75.0ms	(* (* (* i i) 0.5) (log 1.0))
2.0ms	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
2.0ms	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
3.0ms	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))

series10.0s

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (* (* i i) 0.5) (log 1.0))
3.0s	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
3.2s	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
3.5s	(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1979
1	355
0	136

prune761.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.7b

regimes346.0ms

Accuracy

53.9% (10.5b remaining)

Error of 21.5b against oracle of 11.0b and baseline of 33.8b

bsearch278.0ms

Steps

Iters	Range		Point
9	3.0812599035097804e-09	7.830610238325062	4.039962480132393
9	-69051.06592837533	-4.7512835972832904e-05	-0.008529206764181105

simplify5.0ms

Iterations

Iter	Nodes
done	52
1	52
0	37

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.7s	962×	body	2560	valid
2.4s	2469×	body	1280	valid
719.0ms	1584×	body	640	valid
467.0ms	2251×	body	80	nan
260.0ms	3111×	body	80	valid
207.0ms	878×	body	320	valid
107.0ms	451×	body	160	valid
46.0ms	11×	body	5120	valid