Details

sample168.0ms

Algorithm

intervals

Results

68.0ms	94×	body	1280	valid
50.0ms	27×	body	2560	valid
17.0ms	57×	body	640	valid
6.0ms	35×	body	320	valid
5.0ms	1×	body	5120	valid
4.0ms	70×	body	80	valid
3.0ms	89×	body	80	nan
1.0ms	14×	body	160	valid

simplify47.0ms

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	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: 44.9b

Counts

2 → 1

localize10.0ms

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)
4.6b	(pow (+ 1.0 (/ i n)) n)
9.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite92.0ms

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:

33.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
14.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
19.0ms	(/ (- (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)
351.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify72.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune730.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	327	6	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	328	6	334

Merged error: 19.0b

Counts

334 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 (pow i 2) (* (log 1.0) n))
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)))
11.9b	(* (pow i 2) (log 1.0))
17.0b	(/ (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 0.5 (pow i 2) (* (log 1.0) n))
15.0ms	(* 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))

series630.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
224.0ms	(* 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)))
136.0ms	(* (pow i 2) (log 1.0))
205.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify115.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	731	3120
1	3626	2891
2	5002	2891

prune686.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	187	17	204

Merged error: 9.6b

Counts

204 → 17

localize20.0ms

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))))) i) n)
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))
11.2b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.9b	(* (pow i 2) (log 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `log-pow`

Counts

4 → 122

Calls

4 calls:

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)
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))

series708.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
224.0ms	(* 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	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
143.0ms	(* (pow i 2) (log 1.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	476	1783
1	2011	1521
2	5001	1513

prune415.0ms

Filtered

134 candidates to 92 candidates (68.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	134	17	151

Merged error: 9.6b

Counts

151 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

11.9b	(* (pow i 2) (log 1.0))
12.0b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
12.0b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
12.0b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

rewrite11.0ms

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×	`log-prod` `add-cbrt-cube`
5×	`pow1`
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-exp` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

6.0ms	(* (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))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (pow i 2) (log 1.0))
754.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
752.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
739.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	279	1176
1	923	1076
2	5001	1061

prune359.0ms

Filtered

87 candidates to 69 candidates (79.3%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	85	19	104

Merged error: 9.6b

Counts

104 → 19

regimes259.0ms

Accuracy

65.3% (6.3b remaining)

Error of 17.3b against oracle of 11.1b and baseline of 29.1b

bsearch187.0ms

Steps

Iters	Range		Point
10	37.684576067535986	1.2747519734402982e+17	38.49069217280769
2	-9.400999762744531e-24	-8.063011617561731e-24	-9.233751244596682e-24

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	41
1	50	41

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.1s	2923×	body	1280	valid
1.8s	949×	body	2560	valid
553.0ms	1792×	body	640	valid
155.0ms	873×	body	320	valid
118.0ms	2386×	body	80	valid
81.0ms	2150×	body	80	nan
49.0ms	456×	body	160	valid
19.0ms	5×	body	5120	valid