Details

sample190.0ms

Algorithm

intervals

Results

76.0ms	42×	body	2560	valid
61.0ms	71×	body	1280	valid
16.0ms	48×	body	640	valid
9.0ms	92×	body	80	valid
6.0ms	30×	body	320	valid
4.0ms	1×	body	5120	valid
4.0ms	63×	body	80	nan
2.0ms	13×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b	(pow (+ 1.0 (/ i n)) n)
13.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite602.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

243.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
113.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms	(pow (+ 1.0 (/ i n)) n)
215.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
243.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
207.0ms	(pow (+ 1.0 (/ i n)) n)
352.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify58.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune773.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 25.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.4b	(* (pow i 2) (log 1.0))
21.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
143.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
7.0ms	(* (pow i 2) (log 1.0))
135.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series583.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
215.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
143.0ms	(* (pow i 2) (log 1.0))
187.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify143.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	929	3604
1	4818	3341
2	5001	3341

prune679.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
2.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
11.2b	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
11.4b	(* (pow i 2) (log 1.0))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

164×	`times-frac`
127×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
53×	`add-exp-log`
48×	`associate-r`
32×	`add-cbrt-cube`
23×	`div-exp`
21×	`associate-l`
13×	`prod-exp` `associate-/r*`
12×	`cbrt-undiv` `unswap-sqr`
10×	`div-inv`
9×	`add-log-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`unpow-prod-down`
3×	`distribute-rgt-in` `rec-exp` `distribute-lft-in` `1-exp` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `frac-times` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 215

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
133.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
152.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
7.0ms	(* (pow i 2) (log 1.0))

series543.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
154.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
206.0ms	(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
145.0ms	(* (pow i 2) (log 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1153	4367
1	5001	3912

prune702.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
2.6b	(* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n)
11.2b	(* (/ 100.0 i) (- (* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n) (* 0.5 (* (pow i 2) (* (log 1.0) n)))))
11.4b	(* (pow i 2) (* (log 1.0) n))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log` `associate-l`
23×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`prod-exp`
10×	`times-frac`
9×	`add-log-exp`
8×	`pow1`
7×	`associate-r`
6×	`cbrt-unprod`
3×	`unpow-prod-down` `associate-l/` `sum-log` `-commutative` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `associate-*r/` `pow-prod-down` `pow-exp` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `div-exp` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 98

Calls

4 calls:

8.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
30.0ms	(* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n)
67.0ms	(* (/ 100.0 i) (- (* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n) (* 0.5 (* (pow i 2) (* (log 1.0) n)))))
9.0ms	(* (pow i 2) (* (log 1.0) n))

series324.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
57.0ms	(* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n)
150.0ms	(* (/ 100.0 i) (- (* (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) n) (* 0.5 (* (pow i 2) (* (log 1.0) n)))))
71.0ms	(* (pow i 2) (* (log 1.0) n))

simplify87.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	587	1513
1	2821	1345
2	5001	1343

prune299.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

regimes232.0ms

Accuracy

51.7% (10.6b remaining)

Error of 21.6b against oracle of 11.0b and baseline of 33.0b

bsearch316.0ms

Steps

Iters	Range		Point
5	2.6930000565052037e+265	9.367091293497255e+265	5.663291218810887e+265
7	1.0575510317571654e+51	1.2501576144527626e+53	1.2243718320891224e+53
5	4.8244160186105205e-08	1.574218364489979e-07	1.5425208996765195e-07
7	-0.012567608813020674	-0.0006597345534036075	-0.003897370925930358

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	70
1	80	70

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.0s	1015×	body	2560	valid
1.9s	2485×	body	1280	valid
525.0ms	1585×	body	640	valid
208.0ms	3032×	body	80	valid
184.0ms	903×	body	320	valid
115.0ms	2180×	body	80	nan
59.0ms	434×	body	160	valid
14.0ms	4×	body	5120	valid