Details

sample179.0ms

Algorithm

intervals

Results

66.0ms	86×	body	1280	valid
65.0ms	32×	body	2560	valid
21.0ms	65×	body	640	valid
5.0ms	28×	body	320	valid
4.0ms	81×	body	80	valid
3.0ms	67×	body	80	nan
2.0ms	14×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 48.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.5b	(pow (+ 1.0 (/ i n)) n)
11.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite89.0ms

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:

34.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
21.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

374.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
257.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms	(pow (+ 1.0 (/ i n)) n)
355.0ms	(/ (- (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

prune811.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.4b

localize17.0ms

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)))
14.3b	(* (pow i 2) (log 1.0))
21.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite59.0ms

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:

10.0ms	(* 0.5 (pow i 2))
20.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
15.0ms	(/ (- (+ (* 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:

32.0ms	(* 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)))
142.0ms	(* (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))

simplify143.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (23.0ms)

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

prune735.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize18.0ms

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))
13.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.3b	(* (pow i 2) (log 1.0))

rewrite42.0ms

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))
12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.0ms	(* (pow i 2) (log 1.0))

series528.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
221.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
139.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
143.0ms	(* (pow i 2) (log 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (62.0ms)

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

prune379.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
0.0b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
1.8b	(log (exp (* 0.5 (pow i 2))))
14.3b	(* (pow i 2) (log 1.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

12.0ms	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
2.0ms	(log (exp (* 0.5 (pow i 2))))
6.0ms	(* (pow i 2) (log 1.0))

series720.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
219.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
25.0ms	(log (exp (* 0.5 (pow i 2))))
339.0ms	(* (pow i 2) (log 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	469	1581
1	2029	1305
2	5002	1283

prune363.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

regimes174.0ms

Accuracy

68.3% (5.6b remaining)

Error of 16.6b against oracle of 10.9b and baseline of 28.7b

bsearch296.0ms

Steps

Iters	Range		Point
9	5.175139968754377e+19	9.790829469375981e+26	5.2622542467923034e+19
11	-3253.153967321615	-8.303200230518375e-17	-0.0723466983079064

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	34
1	57	34

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	2947×	body	1280	valid
1.9s	986×	body	2560	valid
573.0ms	1803×	body	640	valid
147.0ms	847×	body	320	valid
121.0ms	2461×	body	80	valid
78.0ms	2184×	body	80	nan
48.0ms	442×	body	160	valid
18.0ms	5×	body	5120	valid