Details

sample183.0ms

Algorithm

intervals

Results

78.0ms	95×	body	1280	valid
46.0ms	24×	body	2560	valid
26.0ms	62×	body	640	valid
7.0ms	30×	body	320	valid
5.0ms	73×	body	80	valid
3.0ms	67×	body	80	nan
2.0ms	15×	body	160	valid

simplify42.0ms

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

prune3.0ms

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: 45.5b

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)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.5b	(pow (+ 1.0 (/ i n)) n)
7.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i 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)
7.0ms	(pow (+ 1.0 (/ i n)) n)
20.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series190.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
36.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
63.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune620.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	9	294

Merged error: 19.0b

Counts

294 → 9

localize19.0ms

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)))
12.4b	(* (pow i 2) (log 1.0))
17.8b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite54.0ms

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)))
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))
14.0ms	(/ (- (+ (* 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)))
21.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
16.0ms	(* (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))

simplify143.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (25.0ms)

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

prune946.0ms

Filtered

150 candidates to 198 candidates (-32.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	185	13	198
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	186	21	207

Merged error: 11.0b

Counts

207 → 21

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
11.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.4b	(* (pow i 2) (log 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `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-*l/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

11.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
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))
13.0ms	(/ (- (+ (* 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))

series70.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
21.0ms	(* 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)
12.0ms	(* (pow i 2) (log 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	529	1979
1	2435	1684
2	5001	1679

prune467.0ms

Filtered

87 candidates to 129 candidates (-48.3%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	20	20
Picked	0	1	1
Done	0	0	0
Total	128	22	150

Merged error: 11.0b

Counts

150 → 22

localize32.0ms

Local error

Found 4 expressions with local error:

12.4b	(* (pow i 2) (log 1.0))
12.4b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
12.4b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
12.4b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `cbrt-prod`
8×	`associate-l`
6×	`cbrt-div` `log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `associate-r` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/3` `prod-exp` `flip--`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (pow i 2) (log 1.0))
8.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
8.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
9.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (pow i 2) (log 1.0))
55.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
57.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
59.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	1468
1	1220	1365
2	5002	1347

prune793.0ms

Filtered

70 candidates to 85 candidates (-21.4%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	3	17	20
Picked	1	0	1
Done	0	1	1
Total	85	22	107

Merged error: 11.0b

Counts

107 → 22

regimes711.0ms

Accuracy

68% (5.6b remaining)

Error of 16.3b against oracle of 10.7b and baseline of 28.3b

bsearch134.0ms

Steps

Iters	Range		Point
11	2.1122460899073325e-16	150298.86953896628	0.14346354665808614
3	-0.03797323103254447	-0.030191044061917315	-0.03742065960075011

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	50
1	67	50

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	2995×	body	1280	valid
2.1s	1000×	body	2560	valid
694.0ms	1728×	body	640	valid
212.0ms	876×	body	320	valid
166.0ms	2337×	body	80	valid
96.0ms	2262×	body	80	nan
64.0ms	414×	body	160	valid
34.0ms	9×	body	5120	valid

Details

sample183.0ms

simplify42.0ms

prune3.0ms

localize9.0ms

rewrite87.0ms

series190.0ms

simplify60.0ms

prune620.0ms

localize19.0ms

rewrite54.0ms

series63.0ms

simplify143.0ms

prune946.0ms

localize16.0ms

rewrite46.0ms

series70.0ms

simplify80.0ms

prune467.0ms

localize32.0ms

rewrite34.0ms

series184.0ms

simplify50.0ms

prune793.0ms

regimes711.0ms

bsearch134.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling