Details

sample198.0ms

Algorithm

intervals

Results

79.0ms	100×	body	1280	valid
66.0ms	33×	body	2560	valid
21.0ms	52×	body	640	valid
6.0ms	24×	body	320	valid
6.0ms	75×	body	80	valid
3.0ms	59×	body	80	nan
2.0ms	10×	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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 46.5b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite79.0ms

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)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
15.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series192.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
35.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
65.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune598.0ms

Filtered

293 candidates to 223 candidates (23.9%)

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: 19.5b

Counts

294 → 7

localize16.0ms

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)))
11.1b	(* (pow i 2) (log 1.0))
17.4b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite53.0ms

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:

6.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
18.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
8.0ms	(* (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))

series63.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
24.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.0ms	(* (pow i 2) (log 1.0))
20.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify147.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	929	3604
1	4818	3341
2	5001	3341

prune773.0ms

Filtered

198 candidates to 150 candidates (24.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	188	17	205

Merged error: 9.0b

Counts

205 → 17

localize17.0ms

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))
10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
11.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
10.0ms	(/ (- (+ (* 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))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
23.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.0ms	(* (pow i 2) (log 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	540	1516
1	2465	1293
2	5001	1289

prune312.0ms

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	110	17	127

Merged error: 9.0b

Counts

127 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
2.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
8.3b	(* (/ 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)))
11.1b	(* (pow i 2) (log 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

156×	`add-sqr-sqrt`
121×	`times-frac`
74×	`*-un-lft-identity`
61×	`add-exp-log`
59×	`add-cube-cbrt`
50×	`cbrt-prod`
45×	`associate-l`
37×	`unswap-sqr`
34×	`unpow-prod-down`
26×	`associate-r`
23×	`div-exp` `prod-exp`
17×	`add-cbrt-cube`
11×	`unpow2` `sqr-pow`
7×	`pow1` `pow-to-exp` `pow-exp`
6×	`rec-exp` `log-prod` `1-exp` `associate-/r*`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `div-inv` `associate-/l*`
2×	`*-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 → 215

Calls

4 calls:

1.0ms	(cbrt i)
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
26.0ms	(* (/ 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)))
6.0ms	(* (pow i 2) (log 1.0))

series82.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt i)
26.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
19.0ms	(* (/ 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)))
16.0ms	(* (pow i 2) (log 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1060	4682
1	5001	4210

prune764.0ms

Filtered

227 candidates to 155 candidates (31.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	222	5	227
Fresh	5	10	15
Picked	1	0	1
Done	0	1	1
Total	228	16	244

Merged error: 9.0b

Counts

244 → 16

regimes295.0ms

Accuracy

65.9% (6.0b remaining)

Error of 17.2b against oracle of 11.2b and baseline of 28.8b

bsearch252.0ms

Steps

Iters	Range		Point
9	1.2866293973920758e+218	3.1087436856754645e+227	3.6778071700114373e+224
7	1.9614291287605636e+159	5.5847321221410994e+160	1.550465547166594e+160
8	1.9153266389864453e-19	4.852633474484347e-15	4.7513303566604e-15
7	-9.833889077906356	-0.05940270564741191	-1.1089623011902427

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	49
1	71	49

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	2908×	body	1280	valid
2.1s	1007×	body	2560	valid
750.0ms	1822×	body	640	valid
222.0ms	907×	body	320	valid
171.0ms	2350×	body	80	valid
100.0ms	2319×	body	80	nan
69.0ms	443×	body	160	valid
13.0ms	3×	body	5120	valid

Details

sample198.0ms

simplify41.0ms

prune6.0ms

localize9.0ms

rewrite79.0ms

series192.0ms

simplify60.0ms

prune598.0ms

localize16.0ms

rewrite53.0ms

series63.0ms

simplify147.0ms

prune773.0ms

localize17.0ms

rewrite36.0ms

series57.0ms

simplify76.0ms

prune312.0ms

localize25.0ms

rewrite54.0ms

series82.0ms

simplify66.0ms

prune764.0ms

regimes295.0ms

bsearch252.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling