Details

sample161.0ms

Algorithm

intervals

Results

60.0ms	30×	body	2560	valid
54.0ms	83×	body	1280	valid
18.0ms	56×	body	640	valid
4.0ms	25×	body	320	valid
4.0ms	89×	body	80	valid
4.0ms	1×	body	5120	valid
3.0ms	84×	body	80	nan
1.0ms	15×	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: 43.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b	(pow (+ 1.0 (/ i n)) n)
10.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite551.0ms

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:

225.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
103.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms	(pow (+ 1.0 (/ i n)) n)
194.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

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)
205.0ms	(pow (+ 1.0 (/ i n)) n)
343.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune798.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

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)))
12.1b	(* (pow i 2) (log 1.0))
19.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite277.0ms

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)))
131.0ms	(* 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))
123.0ms	(/ (- (+ (* 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:

44.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
206.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
145.0ms	(* (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

prune690.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
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)
11.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.1b	(* (pow i 2) (log 1.0))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

119.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
137.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
122.0ms	(/ (- (+ (* 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))

series669.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
238.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
136.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms	(* (pow i 2) (log 1.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	540	1985
1	2839	1693
2	5002	1693

prune583.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
7.1b	(* (/ 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)))
9.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
12.1b	(* (pow i 2) (log 1.0))

rewrite333.0ms

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)
176.0ms	(* (/ 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)))
128.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
6.0ms	(* (pow i 2) (log 1.0))

series743.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt i)
222.0ms	(* (/ 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)))
211.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
137.0ms	(* (pow i 2) (log 1.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1683	7623
1	5001	7328

prune1.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.2b

regimes230.0ms

Accuracy

63% (6.7b remaining)

Error of 18.1b against oracle of 11.4b and baseline of 29.4b

bsearch293.0ms

Steps

Iters	Range		Point
5	2.1156019066638916e+289	4.577855936315765e+289	2.745686100596795e+289
10	9.229508149002838e+228	6.473625115333604e+243	2.1790098039426925e+235
7	4.0498830223506504e-24	8.393344074290648e-23	8.303151281634838e-23
8	-5.4793573196899966e-14	-2.1205983461440786e-16	-5.434849520670692e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	53
1	75	53

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2932×	body	1280	valid
1.8s	962×	body	2560	valid
560.0ms	1799×	body	640	valid
158.0ms	892×	body	320	valid
113.0ms	2430×	body	80	valid
82.0ms	2286×	body	80	nan
45.0ms	424×	body	160	valid
22.0ms	6×	body	5120	valid