Details

sample296.0ms

Algorithm

intervals

Results

120.0ms	87×	body	1280	valid
85.0ms	24×	body	2560	valid
34.0ms	52×	body	640	valid
12.0ms	32×	body	320	valid
9.0ms	93×	body	80	valid
6.0ms	80×	body	80	nan
4.0ms	19×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (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:

383.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
243.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(pow (+ 1.0 (/ i n)) n)
450.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts

4 → 12

Calls

4 calls:

569.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
385.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
297.0ms	(pow (+ 1.0 (/ i n)) n)
473.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.5s

Counts

333 → 333

Iterations

Iter	Nodes
done	5000
1	1492
0	479

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.3b

localize44.0ms

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))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
12.1b	(* (* i i) (log 1.0))
18.2b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

rewrite84.0ms

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))
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)))
18.0ms	(* (* i i) (log 1.0))
16.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

series855.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma (* i i) 0.5 (* 1.0 i))
257.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
229.0ms	(* (* i i) (log 1.0))
281.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

simplify2.3s

Counts

193 → 193

Iterations

Iter	Nodes
done	5011
2	3495
1	966
0	324

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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))
0.1b	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)) n)
11.5b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
12.1b	(* (* i i) (log 1.0))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
25×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
17×	`pow1`
10×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
6×	`log-prod`
5×	`associate-l`
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-*r/` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `flip3--` `div-sub` `associate-*l/` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

18.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i))
33.0ms	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)) n)
16.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
22.0ms	(* (* i i) (log 1.0))

series949.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i))
317.0ms	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)) n)
214.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
205.0ms	(* (* i i) (log 1.0))

simplify2.6s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1955
1	583
0	212

prune808.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

localize72.0ms

Local error

Found 4 expressions with local error:

12.1b	(* (* i i) (log 1.0))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
12.2b	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

16.0ms	(* (* i i) (log 1.0))
2.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
2.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
3.0ms	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))

series9.0s

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (* i i) (log 1.0))
2.8s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
2.8s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))
3.1s	(cbrt (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)))

simplify2.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	3830
2	948
1	307
0	124

prune537.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.0b

regimes280.0ms

Accuracy

52.6% (10.8b remaining)

Error of 22.2b against oracle of 11.4b and baseline of 34.2b

bsearch312.0ms

Steps

Iters	Range		Point
7	7.2949686944817395e+205	1.8280591761267005e+208	1.540498293983816e+208
12	9.084828359643272e-19	1.6311032011848909e+25	1.9432388931584246
5	-7.642915086960539e-08	-3.0023583529873386e-08	-7.524185979796087e-08

simplify14.0ms

Iterations

Iter	Nodes
done	66
1	66
0	51

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.2s	2441×	body	1280	valid
2.0s	972×	body	2560	valid
661.0ms	1619×	body	640	valid
205.0ms	3005×	body	80	valid
182.0ms	920×	body	320	valid
151.0ms	2297×	body	80	nan
54.0ms	453×	body	160	valid
33.0ms	9×	body	5120	valid