Details

sample162.0ms

Algorithm

intervals

Results

68.0ms	92×	body	1280	valid
46.0ms	25×	body	2560	valid
18.0ms	56×	body	640	valid
6.0ms	81×	body	80	nan
5.0ms	31×	body	320	valid
5.0ms	98×	body	80	valid
1.0ms	12×	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: 45.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
9.6b	(pow (+ 1.0 (/ i n)) 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:

35.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
7.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

356.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
246.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
355.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
248.0ms	(pow (+ 1.0 (/ i n)) n)

simplify66.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5001	3446

prune862.0ms

Filtered

333 candidates to 242 candidates (72.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	324	9	333
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	325	9	334

Merged error: 18.5b

Counts

334 → 9

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))))) (/ i n)))
0.2b	(fma 0.5 (pow i 2) (* (log 1.0) n))
13.3b	(* (pow i 2) (log 1.0))
20.9b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite48.0ms

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:

21.0ms	(* 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)))
1.0ms	(fma 0.5 (pow i 2) (* (log 1.0) 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))

series598.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(* 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)))
64.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
138.0ms	(* (pow i 2) (log 1.0))
188.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify140.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (17.0ms)

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

prune760.0ms

Filtered

198 candidates to 152 candidates (76.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	186	12	198
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	187	20	207

Merged error: 9.5b

Counts

207 → 20

localize21.0ms

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))))) i) n))
0.2b	(fma 0.5 (pow i 2) (* (log 1.0) n))
12.5b	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
13.3b	(* (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:

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))
1.0ms	(fma 0.5 (pow i 2) (* (log 1.0) 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))

series549.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* 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))
65.0ms	(fma 0.5 (pow i 2) (* (log 1.0) n))
134.0ms	(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms	(* (pow i 2) (log 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	403	1280
1	1640	1087
2	5002	1080

prune381.0ms

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: 9.5b

Counts

130 → 20

localize22.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
13.3b	(* (pow i 2) (log 1.0))
13.3b	(* (pow i 2) (log 1.0))
13.3b	(* (pow i 2) (log 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
24×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `unswap-sqr`
10×	`add-cbrt-cube`
9×	`distribute-rgt-in` `distribute-lft-in` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-to-exp` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod`
1×	`pow1/3`

Counts

4 → 121

Calls

4 calls:

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))))))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

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))))))
139.0ms	(* (pow i 2) (log 1.0))
137.0ms	(* (pow i 2) (log 1.0))
138.0ms	(* (pow i 2) (log 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	910
1	899	820
2	5001	799

prune520.0ms

Filtered

133 candidates to 87 candidates (65.4%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	17	18
Picked	0	1	1
Done	0	1	1
Total	133	20	153

Merged error: 9.5b

Counts

153 → 20

regimes360.0ms

Accuracy

67.4% (6.0b remaining)

Error of 16.6b against oracle of 10.6b and baseline of 29.0b

bsearch266.0ms

Steps

Iters	Range		Point
5	8.187535937152216e+254	2.819161613138082e+255	1.8069577640268902e+255
8	3.5502089212920536e+236	9.207076228271214e+238	3.1676360098591807e+238
7	3.798938191215488e-08	6.341782789262252e-06	6.231696762840839e-06
7	-42.109556907093555	-1.2231809249317622	-1.322648556346116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	67
1	78	67

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.1s	2949×	body	1280	valid
1.8s	944×	body	2560	valid
561.0ms	1808×	body	640	valid
155.0ms	881×	body	320	valid
115.0ms	2325×	body	80	valid
85.0ms	2303×	body	80	nan
48.0ms	406×	body	160	valid
21.0ms	6×	body	5120	valid