Details

sample418.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.340063%

Results

85.0ms	94×	body	1280	valid
82.0ms	35×	body	2560	valid
20.0ms	44×	body	640	valid
7.0ms	25×	body	320	valid
7.0ms	89×	body	80	valid
3.0ms	62×	body	80	nan
2.0ms	12×	body	160	valid

simplify45.0ms

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: 46.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b	(pow (+ 1.0 (/ i n)) n)
12.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite95.0ms

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:

35.0ms	(* 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))

series198.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
37.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
31.0ms	(pow (+ 1.0 (/ i n)) n)
61.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune660.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Merged error: 22.5b

Counts

294 → 6

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)))
11.4b	(* (pow i 2) (log 1.0))
20.2b	(/ (- (+ (* 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:

6.0ms	(* 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))
17.0ms	(/ (- (+ (* 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:

3.0ms	(* 0.5 (pow i 2))
26.0ms	(* 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	(* (pow i 2) (log 1.0))
21.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify157.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (27.0ms)

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

prune859.0ms

Filtered

157 candidates to 212 candidates (-35.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	205	13	218

Merged error: 9.3b

Counts

218 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)
10.7b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b	(* (pow i 2) (log 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-exp-log`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
15×	`associate-r`
12×	`associate-l`
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)
6.0ms	(* (pow i 2) (log 1.0))

series59.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
27.0ms	(* (* 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	(/ (- (+ (* 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))

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	525	1450
1	2621	1228
2	5001	1228

prune348.0ms

Filtered

79 candidates to 124 candidates (-57.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	124	13	137

Merged error: 9.3b

Counts

137 → 13

localize18.0ms

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)))))
2.7b	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
11.4b	(* (pow i 2) (log 1.0))
12.6b	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

11.0ms	(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
12.0ms	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
8.0ms	(* (pow i 2) (log 1.0))
14.0ms	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

series65.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
17.0ms	(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
13.0ms	(* (pow i 2) (log 1.0))
22.0ms	(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

simplify105.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	539	1687
1	3113	1361
2	5001	1336

prune286.0ms

Filtered

78 candidates to 117 candidates (-50.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	117	13	130

Merged error: 9.3b

Counts

130 → 13

regimes232.0ms

Accuracy

65% (6.3b remaining)

Error of 17.1b against oracle of 10.7b and baseline of 28.9b

bsearch308.0ms

Steps

Iters	Range		Point
12	9.383758716671574e+49	1.4644946837027803e+89	9.532360402610846e+49
9	-2.1005547882066785e-05	-2.2613526106276006e-10	-2.076066022483383e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	30
1	57	30

end0.0ms

sample6.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.340063%

Results

2.6s	2913×	body	1280	valid
2.1s	973×	body	2560	valid
755.0ms	1776×	body	640	valid
228.0ms	881×	body	320	valid
195.0ms	2466×	body	80	valid
110.0ms	2311×	body	80	nan
71.0ms	420×	body	160	valid
44.0ms	10×	body	5120	valid

Details

sample418.0ms

simplify45.0ms

prune3.0ms

localize10.0ms

rewrite95.0ms

series198.0ms

simplify66.0ms

prune660.0ms

localize18.0ms

rewrite59.0ms

series63.0ms

simplify157.0ms

prune859.0ms

localize20.0ms

rewrite40.0ms

series59.0ms

simplify89.0ms

prune348.0ms

localize18.0ms

rewrite50.0ms

series65.0ms

simplify105.0ms

prune286.0ms

regimes232.0ms

bsearch308.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling