Details

sample201.0ms

Algorithm

intervals

Results

74.0ms	79×	body	1280	valid
62.0ms	28×	body	2560	valid
23.0ms	54×	body	640	valid
7.0ms	32×	body	320	valid
6.0ms	99×	body	80	valid
3.0ms	58×	body	80	nan
2.0ms	13×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize40.0ms

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)
4.9b	(pow (+ 1.0 (/ i n)) n)
8.9b	(/ (- (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:

401.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
290.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms	(pow (+ 1.0 (/ i n)) n)
434.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

496.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
384.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
333.0ms	(pow (+ 1.0 (/ i n)) n)
551.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.3s

Counts

333 → 333

Iterations

Iter	Nodes
done	5000
1	1492
0	479

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize61.0ms

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)))
8.9b	(* (* i i) (log 1.0))
15.2b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

rewrite88.0ms

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))
40.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
17.0ms	(* (* i i) (log 1.0))
17.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n))

series774.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (* i i) 0.5 (* 1.0 i))
264.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ i n)))
201.0ms	(* (* i i) (log 1.0))
231.0ms	(/ (- (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

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.4b

localize44.0ms

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)
8.4b	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
8.9b	(* (* i i) (log 1.0))

rewrite102.0ms

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:

27.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i))
35.0ms	(* (* 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	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
17.0ms	(* (* i i) (log 1.0))

series813.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i))
241.0ms	(* (* 100.0 (/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)) n)
189.0ms	(/ (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) i)
209.0ms	(* (* i i) (log 1.0))

simplify2.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1955
1	583
0	212

prune649.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 10.4b

localize30.0ms

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)) (/ 1 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)) (/ 1 i))) n)
8.6b	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i))
8.9b	(* (* i i) (log 1.0))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
37×	`add-cbrt-cube`
31×	`prod-exp`
26×	`pow1`
25×	`add-sqr-sqrt`
21×	`associate-r`
19×	`cbrt-unprod`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`associate-*r/`
13×	`pow-prod-down`
12×	`associate-*l/`
11×	`times-frac`
8×	`associate-l`
6×	`frac-times` `log-prod` `flip3--` `div-exp` `flip--`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `cbrt-undiv` `rec-exp` `distribute-lft-in` `1-exp` `un-div-inv`
1×	`log-pow` `div-inv`

Counts

4 → 133

Calls

4 calls:

30.0ms	(* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i)))
95.0ms	(* (* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i))) n)
27.0ms	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i))
16.0ms	(* (* i i) (log 1.0))

series949.0ms

Counts

4 → 12

Calls

4 calls:

426.0ms	(* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i)))
209.0ms	(* (* 100.0 (* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i))) n)
155.0ms	(* (- (fma n (log 1.0) (fma (* i i) 0.5 (* 1.0 i))) (* (* (* i i) (log 1.0)) 0.5)) (/ 1 i))
159.0ms	(* (* i i) (log 1.0))

simplify1.8s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
2	2355
1	694
0	245

prune647.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.4b

regimes299.0ms

Accuracy

55% (9.9b remaining)

Error of 21.1b against oracle of 11.2b and baseline of 33.2b

bsearch782.0ms

Steps

Iters	Range		Point
10	4.5367458640904006e+33	2.4397352996973322e+45	4.586135949800823e+33
10	4.625956238950403e-119	1.9886031544758863e-109	1.1504506501799242e-111
5	6.347248424975081e-300	2.0287964304848516e-299	8.94230397278424e-300
9	-0.03438460291724579	-4.6633494757659894e-11	-0.01274350772906005

simplify25.0ms

Iterations

Iter	Nodes
done	81
4	81
3	78
2	71
1	67
0	50

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.3s	2575×	body	1280	valid
2.0s	917×	body	2560	valid
1.1s	1578×	body	640	valid
323.0ms	3075×	body	80	valid
230.0ms	879×	body	320	valid
139.0ms	2237×	body	80	nan
64.0ms	457×	body	160	valid
42.0ms	9×	body	5120	valid