Details

sample215.0ms

Algorithm

intervals

Results

79.0ms	38×	body	2560	valid
77.0ms	88×	body	1280	valid
26.0ms	61×	body	640	valid
7.0ms	24×	body	320	valid
6.0ms	81×	body	80	valid
3.0ms	82×	body	80	nan
3.0ms	19×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	60	7
2	145	7
3	364	7
4	1248	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: 48.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.9b	(pow (+ 1.0 (/ i n)) n)
11.6b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
305×	`add-sqr-sqrt`
222×	`*-un-lft-identity`
156×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
48×	`unpow-prod-down`
33×	`sqr-pow`
28×	`distribute-lft-out--`
24×	`prod-diff`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
8×	`fma-neg`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `log1p-expm1-u`
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`

Counts

4 → 321

Calls

4 calls:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
20.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

349.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
240.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms	(pow (+ 1.0 (/ i n)) n)
489.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune749.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	326	8	334

Merged error: 25.0b

Counts

334 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
12.8b	(* (pow i 2) (log 1.0))
20.6b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite36.0ms

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`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `fma-udef`

Counts

4 → 186

Calls

4 calls:

1.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
13.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 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))
5.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series629.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
210.0ms	(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
137.0ms	(* (pow i 2) (log 1.0))
190.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify118.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	734	3209
1	3750	2968
2	5001	2968

prune671.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	187	11	198
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	188	18	206

Merged error: 13.1b

Counts

206 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.4b	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
12.1b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.8b	(* (pow i 2) (log 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`add-exp-log`
18×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-l`
8×	`prod-exp`
7×	`associate-r`
6×	`log-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-r/` `associate-l/` `pow-exp` `clear-num` `log-pow` `fma-udef` `div-inv`

Counts

4 → 98

Calls

4 calls:

1.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
7.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
3.0ms	(/ (fma i 1.0 (- (fma 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))

series583.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
209.0ms	(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
143.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
138.0ms	(* (pow i 2) (log 1.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	413	1370
1	1888	1165
2	5002	1158

prune331.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	109	19	128

Merged error: 13.1b

Counts

128 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

12.1b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.8b	(* (pow i 2) (log 1.0))
12.8b	(* (pow i 2) (log 1.0))
12.8b	(* (pow i 2) (log 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
21×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r` `log-pow` `-commutative` `cbrt-unprod` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 137

Calls

4 calls:

3.0ms	(/ (fma i 1.0 (- (fma 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))
6.0ms	(* (pow i 2) (log 1.0))
7.0ms	(* (pow i 2) (log 1.0))

series552.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
137.0ms	(* (pow i 2) (log 1.0))
138.0ms	(* (pow i 2) (log 1.0))
144.0ms	(* (pow i 2) (log 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	238	1134
1	868	1013
2	5001	998

prune530.0ms

Filtered

149 candidates to 97 candidates (65.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	149	19	168

Merged error: 13.1b

Counts

168 → 19

regimes259.0ms

Accuracy

67.3% (5.9b remaining)

Error of 16.9b against oracle of 11.1b and baseline of 29.0b

bsearch413.0ms

Steps

Iters	Range		Point
10	7.629039058740419e+233	7.270730595144126e+244	1.3062037450785406e+237
8	1.9089654662209593e+215	2.9433706276129134e+218	3.608822286559413e+217
9	3.411298787602904e-05	14.716166499582775	0.3432321998668171
9	-88.04257933538071	-1.9422237324525578e-06	-0.2700094562738983

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	113
1	84	113

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	2958×	body	1280	valid
2.2s	1033×	body	2560	valid
724.0ms	1748×	body	640	valid
226.0ms	906×	body	320	valid
177.0ms	2348×	body	80	valid
96.0ms	2300×	body	80	nan
65.0ms	418×	body	160	valid
30.0ms	8×	body	5120	valid