Details

sample167.0ms

Algorithm

intervals

Results

64.0ms	81×	body	1280	valid
51.0ms	24×	body	2560	valid
24.0ms	70×	body	640	valid
5.0ms	27×	body	320	valid
5.0ms	80×	body	80	valid
4.0ms	69×	body	80	nan
2.0ms	13×	body	160	valid

simplify43.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 46.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.5b	(pow (+ 1.0 (/ i n)) n)

rewrite87.0ms

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:

33.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
347.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
209.0ms	(pow (+ 1.0 (/ i n)) n)

simplify67.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune737.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	7	294

Merged error: 19.2b

Counts

294 → 7

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)))
12.1b	(* (pow i 2) (log 1.0))
16.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite55.0ms

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:

5.0ms	(* 0.5 (pow i 2))
19.0ms	(* 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))
13.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series769.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 0.5 (pow i 2))
395.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
163.0ms	(* (pow i 2) (log 1.0))
186.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify145.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

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

prune696.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	198	14	212
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	199	20	219

Merged error: 11.7b

Counts

219 → 20

localize19.0ms

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))
0.3b	(* (* 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	(/ (- (+ (* 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))

rewrite44.0ms

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:

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))
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)
6.0ms	(* (pow i 2) (log 1.0))

series629.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
205.0ms	(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
138.0ms	(/ (- (+ (* 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))

simplify85.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (16.0ms)

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

prune351.0ms

Filtered

129 candidates to 86 candidates (66.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	129	20	149

Merged error: 11.7b

Counts

149 → 20

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
7.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
8.1b	(* (/ 1 (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)))
12.1b	(* (pow i 2) (log 1.0))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
321×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`add-exp-log`
94×	`cbrt-prod`
75×	`associate-r`
51×	`div-exp`
48×	`unswap-sqr`
45×	`associate-l`
38×	`unpow-prod-down`
33×	`prod-exp`
29×	`add-cbrt-cube`
22×	`associate-/r*`
13×	`unpow2` `sqr-pow`
12×	`cbrt-undiv`
10×	`pow-to-exp` `pow-exp` `div-inv`
9×	`rec-exp` `1-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`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 → 354

Calls

4 calls:

1.0ms	(cbrt i)
16.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
64.0ms	(* (/ 1 (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)))
6.0ms	(* (pow i 2) (log 1.0))

series768.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt i)
213.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
213.0ms	(* (/ 1 (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)))
145.0ms	(* (pow i 2) (log 1.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

366 → 366

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1793	8813
1	5001	8392

prune1.3s

Filtered

366 candidates to 270 candidates (73.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	359	7	366
Fresh	5	13	18
Picked	1	0	1
Done	0	1	1
Total	365	21	386

Merged error: 11.7b

Counts

386 → 21

regimes403.0ms

Accuracy

68.4% (5.8b remaining)

Error of 16.6b against oracle of 10.8b and baseline of 29.1b

bsearch444.0ms

Steps

Iters	Range		Point
10	5.120978258446056e+119	1.3096497762430056e+132	4.5860988436327915e+126
9	5.6848229271942865e+19	3.0004367998518743e+25	5.753314805691298e+19
8	-225.5047040817839	-0.14827578458452542	-0.677510041185843

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	67
1	71	67

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.3s	2945×	body	1280	valid
1.9s	952×	body	2560	valid
598.0ms	1698×	body	640	valid
190.0ms	918×	body	320	valid
147.0ms	2451×	body	80	valid
109.0ms	2223×	body	80	nan
60.0ms	464×	body	160	valid
11.0ms	3×	body	5120	valid