Details

sample163.0ms

Algorithm

intervals

Results

65.0ms	35×	body	2560	valid
54.0ms	79×	body	1280	valid
20.0ms	68×	body	640	valid
5.0ms	32×	body	320	valid
4.0ms	87×	body	80	valid
2.0ms	72×	body	80	nan
1.0ms	11×	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: 45.8b

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)))
0.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b	(pow (+ 1.0 (/ i n)) n)
11.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite90.0ms

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:

32.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
10.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
432.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
223.0ms	(pow (+ 1.0 (/ i n)) n)
353.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify73.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune748.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	326	7	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	327	7	334

Merged error: 26.1b

Counts

334 → 7

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)))
11.1b	(* (pow i 2) (log 1.0))
19.0b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite35.0ms

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)))))
14.0ms	(* 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)))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series646.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
221.0ms	(* 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)))
133.0ms	(* (pow i 2) (log 1.0))
197.0ms	(/ (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

prune693.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	184	14	198
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	185	20	205

Merged error: 14.2b

Counts

205 → 20

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))
10.5b	(/ (fma i 1.0 (- (fma 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))

rewrite19.0ms

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`
8×	`prod-exp`
6×	`log-prod` `cbrt-unprod`
5×	`associate-r`
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)))))
6.0ms	(* 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))

series599.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
220.0ms	(* 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))
142.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
139.0ms	(* (pow i 2) (log 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	407	1375
1	1669	1164
2	5001	1157

prune341.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	110	20	130

Merged error: 14.2b

Counts

130 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
5.8b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
6.3b	(/ (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (/ (cbrt i) n))
11.1b	(* (pow i 2) (log 1.0))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

2290×	`times-frac`
1017×	`add-sqr-sqrt`
1011×	`add-cube-cbrt` `*-un-lft-identity`
564×	`cbrt-prod`
442×	`unpow-prod-down`
75×	`unpow2` `sqr-pow`
63×	`div-inv`
40×	`associate-/l*`
38×	`add-exp-log`
33×	`associate-/r*`
21×	`div-exp`
18×	`add-cbrt-cube`
9×	`cbrt-undiv`
8×	`associate-l`
6×	`log-prod`
5×	`pow1`
4×	`expm1-log1p-u` `pow-to-exp` `associate-r` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
2×	`frac-2neg` `clear-num`
1×	`pow1/3` `associate-/r/` `log-pow` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 1011

Calls

4 calls:

1.0ms	(cbrt i)
6.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
32.0ms	(/ (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (/ (cbrt i) n))
6.0ms	(* (pow i 2) (log 1.0))

series769.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt i)
204.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
242.0ms	(/ (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (/ (cbrt i) n))
143.0ms	(* (pow i 2) (log 1.0))

simplify351.0ms

Algorithm

egg-herbie

Counts

1023 → 1023

Iterations

Useful iterations: 1 (69.0ms)

Iter	Nodes	Cost
0	4830	33474
1	5001	33099

prune4.1s

Filtered

1023 candidates to 731 candidates (71.5%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	1013	10	1023
Fresh	7	11	18
Picked	1	0	1
Done	0	1	1
Total	1021	22	1043

Merged error: 14.2b

Counts

1043 → 22

regimes302.0ms

Accuracy

66.1% (6.1b remaining)

Error of 17.3b against oracle of 11.2b and baseline of 29.2b

bsearch193.0ms

Steps

Iters	Range		Point
9	1.3261300952414648e-20	8.815605325869767e-16	8.746094629864195e-16
8	-1.1902930357079885e-07	-1.3081950593114417e-10	-1.1787990607175087e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	29
1	43	29

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.0s	2947×	body	1280	valid
1.8s	989×	body	2560	valid
534.0ms	1773×	body	640	valid
144.0ms	853×	body	320	valid
107.0ms	2425×	body	80	valid
77.0ms	2296×	body	80	nan
44.0ms	434×	body	160	valid
40.0ms	11×	body	5120	valid