Details

sample180.0ms

Algorithm

intervals

Results

69.0ms	96×	body	1280	valid
69.0ms	32×	body	2560	valid
16.0ms	50×	body	640	valid
5.0ms	30×	body	320	valid
4.0ms	81×	body	80	valid
2.0ms	74×	body	80	nan
1.0ms	14×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	7
1	60	7
2	145	7
3	364	7
4	1248	7
5	5002	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: 47.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.4b	(pow (+ 1.0 (/ i n)) n)
11.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

329×	`times-frac`
322×	`add-sqr-sqrt`
239×	`*-un-lft-identity`
168×	`add-cube-cbrt`
104×	`associate-r`
87×	`difference-of-squares`
49×	`unpow-prod-down`
34×	`sqr-pow`
32×	`associate-/r*`
30×	`distribute-lft-out--`
25×	`associate-*r/`
24×	`prod-diff`
22×	`associate-/l*`
19×	`add-exp-log`
18×	`associate-/r/` `add-cbrt-cube` `div-inv`
8×	`fma-neg`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
5×	`clear-num` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `associate-/l/`
3×	`pow-unpow` `flip3--` `associate-l` `prod-exp` `un-div-inv` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `*-commutative`

Counts

4 → 364

Calls

4 calls:

41.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
19.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

392.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
263.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
224.0ms	(pow (+ 1.0 (/ i n)) n)
375.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify79.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1424	4013
1	5001	3723

prune777.0ms

Filtered

376 candidates to 273 candidates (72.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	369	7	376
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	370	7	377

Merged error: 22.9b

Counts

377 → 7

localize16.0ms

Local error

Found 3 expressions with local error:

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)))

11.6b

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

19.5b

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
113×	`add-sqr-sqrt`
99×	`*-un-lft-identity`
98×	`add-cube-cbrt`
56×	`associate-r`
32×	`associate-/r*`
22×	`add-exp-log`
19×	`associate-*r/` `add-cbrt-cube`
18×	`associate-/r/`
13×	`associate-/l*`
11×	`associate-l`
10×	`div-inv`
8×	`pow1`
7×	`unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
5×	`clear-num`
4×	`unpow-prod-down` `frac-2neg` `cbrt-unprod`
3×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `un-div-inv` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow`

Counts

3 → 213

Calls

3 calls:

18.0ms

(* 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)))

10.0ms

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

7.0ms

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

series584.0ms

Counts

3 → 9

Calls

3 calls:

236.0ms

(* 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))

211.0ms

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

simplify155.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	789	3489
1	3989	3263
2	5001	3263

prune686.0ms

Filtered

222 candidates to 169 candidates (76.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	210	12	222
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	211	18	229

Merged error: 10.6b

Counts

229 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

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))))))
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	(/ (* 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)
11.6b	(* (pow i 2) (log 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 207

Calls

4 calls:

4.0ms	(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
19.0ms	(* (/ (* 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)
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)
7.0ms	(* (pow i 2) (log 1.0))

series681.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
237.0ms	(* (/ (* 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)
162.0ms	(/ (* 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)
144.0ms	(* (pow i 2) (log 1.0))

simplify145.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	721	3065
1	3920	2796
2	5002	2796

prune645.0ms

Filtered

219 candidates to 161 candidates (73.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	218	19	237

Merged error: 10.6b

Counts

237 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

11.6b	(* (pow i 2) (log 1.0))
11.8b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
11.8b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
11.8b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

rewrite13.0ms

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`
7×	`pow1`
6×	`log-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-r` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `prod-exp`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

7.0ms	(* (pow i 2) (log 1.0))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
1.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (pow i 2) (log 1.0))
846.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
799.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
798.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	279	1179
1	923	1079
2	5002	1064

prune370.0ms

Filtered

88 candidates to 69 candidates (78.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	16	17
Picked	1	0	1
Done	0	1	1
Total	87	20	107

Merged error: 10.6b

Counts

107 → 20

regimes708.0ms

Accuracy

65.1% (6.3b remaining)

Error of 17.4b against oracle of 11.1b and baseline of 29.1b

bsearch441.0ms

Steps

Iters	Range		Point
8	1.1041122235818434e+43	1.550445775864617e+46	1.1157873681258683e+43
8	-5.836795344528573e-218	-5.275162429883666e-221	-5.74741920387597e-218
9	-0.05767290693153419	-6.132196241634436e-08	-0.001601341064536709

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	41
1	49	41

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.1s	2929×	body	1280	valid
1.9s	944×	body	2560	valid
570.0ms	1805×	body	640	valid
159.0ms	894×	body	320	valid
126.0ms	2410×	body	80	valid
83.0ms	2268×	body	80	nan
53.0ms	476×	body	160	valid
28.0ms	7×	body	5120	valid