Details

sample171.0ms

Algorithm

intervals

Results

66.0ms	36×	body	2560	valid
66.0ms	89×	body	1280	valid
14.0ms	44×	body	640	valid
5.0ms	34×	body	320	valid
3.0ms	83×	body	80	valid
2.0ms	76×	body	80	nan
1.0ms	14×	body	160	valid

simplify40.0ms

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: 46.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)
11.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite577.0ms

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:

235.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
108.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
205.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

360.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms	(pow (+ 1.0 (/ i n)) n)
350.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune776.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)))
9.9b	(* (pow i 2) (log 1.0))
19.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
140.0ms	(* 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))
133.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series578.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
213.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
144.0ms	(* (pow i 2) (log 1.0))
196.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify150.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune730.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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))
9.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.9b	(* (pow i 2) (log 1.0))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-r`
11×	`prod-exp`
10×	`pow1`
9×	`times-frac`
8×	`unpow-prod-down` `unswap-sqr`
7×	`cbrt-unprod`
6×	`log-prod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `pow-to-exp` `div-exp` `pow-exp` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `associate-l/` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 112

Calls

4 calls:

6.0ms	(* 0.5 (pow i 2))
105.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
132.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms	(* (pow i 2) (log 1.0))

series529.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* 0.5 (pow i 2))
212.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
142.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
144.0ms	(* (pow i 2) (log 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	518	1449
1	2468	1227
2	5001	1223

prune383.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
6.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
9.3b	(* (/ 100.0 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
9.9b	(* (pow i 2) (log 1.0))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

341×	`times-frac`
264×	`add-sqr-sqrt`
168×	`add-cube-cbrt` `*-un-lft-identity`
85×	`cbrt-prod`
75×	`associate-r`
56×	`add-exp-log`
45×	`associate-l`
30×	`unpow-prod-down`
29×	`add-cbrt-cube`
28×	`unswap-sqr`
24×	`div-exp`
22×	`associate-/r*`
15×	`prod-exp`
12×	`cbrt-undiv`
10×	`div-inv`
9×	`unpow2` `sqr-pow`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`pow-to-exp` `pow-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `flip--`

Counts

4 → 316

Calls

4 calls:

1.0ms	(cbrt i)
134.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
190.0ms	(* (/ 100.0 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
7.0ms	(* (pow i 2) (log 1.0))

series803.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt i)
228.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
240.0ms	(* (/ 100.0 (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
149.0ms	(* (pow i 2) (log 1.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1685	7651
1	5001	7328

prune1.5s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.5b

regimes409.0ms

Accuracy

55.7% (10.0b remaining)

Error of 21.3b against oracle of 11.4b and baseline of 33.9b

bsearch215.0ms

Steps

Iters	Range		Point
9	3.233625039177592e-11	0.003342748024832997	0.0030890666332557444
9	-40603.17280191813	-0.00667476531596465	-0.31883140503528035

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	32
1	50	32

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.8s	978×	body	2560	valid
1.8s	2479×	body	1280	valid
468.0ms	1638×	body	640	valid
141.0ms	844×	body	320	valid
132.0ms	3088×	body	80	valid
73.0ms	2284×	body	80	nan
45.0ms	449×	body	160	valid
16.0ms	5×	body	5120	valid