Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 17.684937%

Guaranteed chance to sample good point: 88.521855%

Results

72.0ms	88×	body	1280	valid
70.0ms	32×	body	2560	valid
20.0ms	49×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	1×	body	5120	valid
5.0ms	6×	body	1280	invalid
4.0ms	54×	body	80	valid
3.0ms	6×	body	640	invalid
2.0ms	8×	body	320	invalid
2.0ms	23×	body	80	invalid
1.0ms	7×	body	160	valid
1.0ms	3×	body	160	invalid
1.0ms	10×	body	80	nan

simplify46.0ms

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: 46.0b

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)))
1.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (- (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:

32.0ms	(* 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))

series191.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
36.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)
65.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune646.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

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: 18.0b

Counts

294 → 7

localize18.0ms

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)))
10.6b	(* (pow i 2) (log 1.0))
17.6b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite63.0ms

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:

7.0ms	(+ (* 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)))
7.0ms	(* (pow i 2) (log 1.0))
16.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series67.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 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)))
13.0ms	(* (pow i 2) (log 1.0))
23.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify171.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (32.0ms)

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

prune895.0ms

Filtered

150 candidates to 198 candidates (-32.0%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	188	10	198
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	189	16	205

Merged error: 7.8b

Counts

205 → 16

localize18.0ms

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))
10.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.6b	(* (pow i 2) (log 1.0))

rewrite45.0ms

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:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
13.0ms	(* 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)
7.0ms	(* (pow i 2) (log 1.0))

series59.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
22.0ms	(* 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))

simplify94.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (74.0ms)

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

prune354.0ms

Filtered

72 candidates to 110 candidates (-52.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	110	16	126

Merged error: 7.8b

Counts

126 → 16

localize28.0ms

Local error

Found 4 expressions with local error:

10.6b	(* (pow i 2) (log 1.0))
10.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
10.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
10.8b	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite40.0ms

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:

7.0ms	(* (pow i 2) (log 1.0))
11.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
10.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
10.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (pow i 2) (log 1.0))
60.0ms	(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)))))
62.0ms	(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

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

prune886.0ms

Filtered

70 candidates to 85 candidates (-21.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	14	14
Picked	1	0	1
Done	0	1	1
Total	85	16	101

Merged error: 7.8b

Counts

101 → 16

regimes552.0ms

Accuracy

69.8% (5.6b remaining)

Error of 16.0b against oracle of 10.4b and baseline of 28.8b

bsearch239.0ms

Steps

Iters	Range		Point
12	7.758043995828473e-12	2.7324892073549815e+45	1.5120834945497763
9	-16.011709609627676	-4.874582257449802e-06	-0.39780581747886845

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	22
1	45	22

end0.0ms

sample7.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 17.684937%

Guaranteed chance to sample good point: 88.521855%

Results

2.4s	2755×	body	1280	valid
2.2s	1026×	body	2560	valid
659.0ms	1571×	body	640	valid
175.0ms	703×	body	320	valid
120.0ms	1628×	body	80	valid
117.0ms	227×	body	640	invalid
95.0ms	111×	body	1280	invalid
78.0ms	860×	body	80	invalid
52.0ms	159×	body	320	invalid
47.0ms	312×	body	160	valid
26.0ms	13×	body	2560	invalid
22.0ms	5×	body	5120	valid
21.0ms	109×	body	160	invalid
10.0ms	200×	body	80	nan

Details

sample1.2s

simplify46.0ms

prune3.0ms

localize9.0ms

rewrite87.0ms

series191.0ms

simplify66.0ms

prune646.0ms

localize18.0ms

rewrite63.0ms

series67.0ms

simplify171.0ms

prune895.0ms

localize18.0ms

rewrite45.0ms

series59.0ms

simplify94.0ms

prune354.0ms

localize28.0ms

rewrite40.0ms

series195.0ms

simplify60.0ms

prune886.0ms

regimes552.0ms

bsearch239.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling