Details

sample185.0ms

Algorithm

intervals

Results

71.0ms	40×	body	2560	valid
68.0ms	92×	body	1280	valid
20.0ms	54×	body	640	valid
6.0ms	31×	body	320	valid
3.0ms	73×	body	80	valid
3.0ms	80×	body	80	nan
2.0ms	15×	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: 48.7b

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)))
1.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
12.9b	(/ (- (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:

35.0ms	(* 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)
18.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
245.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
210.0ms	(pow (+ 1.0 (/ i n)) n)
480.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify70.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune867.0ms

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: 23.5b

Counts

334 → 8

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)))))
0.1b	(* 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))
21.4b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite41.0ms

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)))))
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)))
7.0ms	(* (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))

series653.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
213.0ms	(* 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	(* (pow i 2) (log 1.0))
201.0ms	(/ (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 (19.0ms)

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

prune725.0ms

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: 10.1b

Counts

206 → 18

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))
11.3b	(/ (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))

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`
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)))))
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)
7.0ms	(* (pow i 2) (log 1.0))

series588.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
213.0ms	(* 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)
139.0ms	(* (pow i 2) (log 1.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

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

prune378.0ms

Filtered

110 candidates to 74 candidates (67.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	111	17	128

Merged error: 10.1b

Counts

128 → 17

localize21.0ms

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))))))

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`
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:

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))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (pow i 2) (log 1.0))
730.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
725.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
724.0ms	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	279	1170
1	893	1076
2	5002	1061

prune401.0ms

Filtered

87 candidates to 69 candidates (79.3%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	84	20	104

Merged error: 10.1b

Counts

104 → 20

regimes252.0ms

Accuracy

65.5% (6.0b remaining)

Error of 17.1b against oracle of 11.0b and baseline of 28.5b

bsearch246.0ms

Steps

Iters	Range		Point
9	3.775313734612271e+22	1.9235933371893114e+28	3.8426241943682245e+22
9	-16.884994322593744	-1.4365382038701608e-08	-0.0749921289443251

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	20
1	41	20

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	3009×	body	1280	valid
2.0s	1030×	body	2560	valid
548.0ms	1752×	body	640	valid
162.0ms	912×	body	320	valid
115.0ms	2337×	body	80	valid
80.0ms	2324×	body	80	nan
41.0ms	393×	body	160	valid
29.0ms	8×	body	5120	valid