Details

sample191.0ms

Algorithm

intervals

Results

77.0ms	85×	body	1280	valid
57.0ms	27×	body	2560	valid
20.0ms	52×	body	640	valid
8.0ms	96×	body	80	valid
7.0ms	26×	body	320	valid
4.0ms	64×	body	80	nan
3.0ms	19×	body	160	valid

simplify44.0ms

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: 44.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b	(pow (+ 1.0 (/ i n)) n)
9.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite603.0ms

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:

244.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
112.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms	(pow (+ 1.0 (/ i n)) n)
213.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

387.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
220.0ms	(pow (+ 1.0 (/ i n)) n)
354.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify61.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune879.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

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)))
10.9b	(* (pow i 2) (log 1.0))
18.4b	(/ (- (+ (* 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`
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))
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))
136.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series579.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
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))
196.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify152.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

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

prune767.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

localize16.0ms

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)
10.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.9b	(* (pow i 2) (log 1.0))

rewrite425.0ms

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:

130.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
148.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
133.0ms	(/ (- (+ (* 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))

series662.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
217.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
148.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
139.0ms	(* (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

prune441.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.3b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.9b	(* (pow i 2) (log 1.0))
10.9b	(* (pow i 2) (log 1.0))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `times-frac`
16×	`associate-l`
12×	`log-prod` `add-cbrt-cube`
8×	`unpow-prod-down` `associate-r` `unswap-sqr`
6×	`pow1` `distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate-/r` `associate-/l`
4×	`associate-/l/` `unpow2` `add-log-exp` `sqr-pow`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `div-sub` `div-exp` `pow-exp` `clear-num` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 128

Calls

4 calls:

131.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
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))
7.0ms	(* (pow i 2) (log 1.0))

series570.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
138.0ms	(/ (- (+ (* 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))
147.0ms	(* (pow i 2) (log 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	300	1714
1	1278	1540
2	5002	1522

prune552.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.1b

regimes419.0ms

Accuracy

49.4% (11.5b remaining)

Error of 22.2b against oracle of 10.8b and baseline of 33.4b

bsearch602.0ms

Steps

Iters	Range		Point
8	9.905379659133977e-173	2.410908475436866e-169	2.0850330521039454e-172
10	-1.308610303336602e-202	-1.224995290711999e-214	-1.2431085101949388e-214
9	-8.085901714425178e+20	-317207061041.6537	-3.514216942264821e+16
5	-1.8966346348049942e+86	-4.88873892774292e+85	-1.0958004164778634e+86
9	-2.601267202579393e+142	-2.2079686958706775e+136	-2.2308731815162504e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	118
1	70	118

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.1s	1008×	body	2560	valid
2.1s	2434×	body	1280	valid
648.0ms	1594×	body	640	valid
268.0ms	3083×	body	80	valid
230.0ms	892×	body	320	valid
143.0ms	2193×	body	80	nan
76.0ms	444×	body	160	valid
16.0ms	5×	body	5120	valid