Details

sample186.0ms

Algorithm

intervals

Results

73.0ms	38×	body	2560	valid
70.0ms	95×	body	1280	valid
16.0ms	53×	body	640	valid
5.0ms	26×	body	320	valid
4.0ms	83×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	74×	body	80	nan
1.0ms	9×	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: 49.6b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b	(pow (+ 1.0 (/ i n)) n)
11.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite96.0ms

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)
7.0ms	(pow (+ 1.0 (/ i n)) n)
21.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

369.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
208.0ms	(pow (+ 1.0 (/ i n)) n)
344.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune737.0ms

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: 23.0b

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)))
9.9b	(* (pow i 2) (log 1.0))
19.1b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite39.0ms

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)))
9.0ms	(* (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))

series699.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
233.0ms	(* 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)))
139.0ms	(* (pow i 2) (log 1.0))
207.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify116.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (19.0ms)

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

prune669.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	191	7	198
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	192	14	206

Merged error: 10.6b

Counts

206 → 14

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))
9.3b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
9.9b	(* (pow i 2) (log 1.0))

rewrite23.0ms

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)
10.0ms	(* (pow i 2) (log 1.0))

series604.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
223.0ms	(* 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))
140.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms	(* (pow i 2) (log 1.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	406	1369
1	1734	1164
2	5003	1157

prune319.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	110	14	124

Merged error: 10.6b

Counts

124 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt i)
5.6b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
8.7b	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
9.9b	(* (pow i 2) (log 1.0))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
321×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`add-exp-log`
94×	`cbrt-prod`
75×	`associate-r`
51×	`div-exp`
48×	`unswap-sqr`
45×	`associate-l`
38×	`unpow-prod-down`
33×	`prod-exp`
29×	`add-cbrt-cube`
22×	`associate-/r*`
13×	`unpow2` `sqr-pow`
12×	`cbrt-undiv`
10×	`pow-to-exp` `pow-exp` `div-inv`
9×	`rec-exp` `1-exp`
7×	`pow1` `cbrt-unprod`
6×	`log-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`frac-times` `frac-2neg` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `log-pow`

Counts

4 → 359

Calls

4 calls:

1.0ms	(cbrt i)
8.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
56.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
6.0ms	(* (pow i 2) (log 1.0))

series787.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt i)
228.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
230.0ms	(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n)))
143.0ms	(* (pow i 2) (log 1.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1644	7943
1	5001	7529

prune1.4s

Filtered

371 candidates to 273 candidates (73.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	369	2	371
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	370	15	385

Merged error: 10.6b

Counts

385 → 15

regimes334.0ms

Accuracy

65% (6.3b remaining)

Error of 17.2b against oracle of 10.9b and baseline of 28.8b

bsearch344.0ms

Steps

Iters	Range		Point
10	7.850449796834028e+120	3.2610480895807413e+136	4.129685281672301e+131
11	2.1659491043976583e-29	1.8364001780596707e-08	4.4408729626575344e-11
10	-0.003816194045177074	-2.2166682569578767e-15	-0.003777373761230917

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	36
1	55	36

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	2915×	body	1280	valid
1.9s	1017×	body	2560	valid
525.0ms	1739×	body	640	valid
151.0ms	911×	body	320	valid
118.0ms	2500×	body	80	valid
85.0ms	2384×	body	80	nan
47.0ms	432×	body	160	valid
34.0ms	9×	body	5120	valid