Details

sample157.0ms

Algorithm

intervals

Results

72.0ms	38×	body	2560	valid
50.0ms	67×	body	1280	valid
11.0ms	43×	body	640	valid
5.0ms	32×	body	320	valid
4.0ms	102×	body	80	valid
2.0ms	74×	body	80	nan
1.0ms	15×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b	(pow (+ 1.0 (/ i n)) n)
12.1b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
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` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

219.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
101.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
192.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

426.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
238.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms	(pow (+ 1.0 (/ i n)) n)
336.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune767.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
0.1b	(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
1.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b	(pow (+ 1.0 (/ i n)) n)

rewrite711.0ms

Algorithm

rewrite-expression-head

Rules

1689×	`times-frac`
1097×	`add-sqr-sqrt`
830×	`*-un-lft-identity`
662×	`add-cube-cbrt`
330×	`associate-r`
246×	`difference-of-squares`
86×	`unpow-prod-down`
83×	`sqr-pow`
82×	`distribute-lft-out--`
80×	`div-inv`
59×	`add-exp-log`
34×	`add-cbrt-cube`
32×	`div-exp`
25×	`associate-/l*`
16×	`cbrt-undiv`
13×	`associate-/r*`
9×	`prod-exp`
7×	`pow1` `unswap-sqr`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`rec-exp` `1-exp`
3×	`pow-unpow` `associate-l`
2×	`div-sub` `associate-/r/`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `flip--` `associate-/l/` `distribute-lft-out`

Counts

4 → 786

Calls

4 calls:

347.0ms	(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
182.0ms	(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
102.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
366.0ms	(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
282.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms	(pow (+ 1.0 (/ i n)) n)

simplify155.0ms

Algorithm

egg-herbie

Counts

798 → 798

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	3132	11388
1	5001	10920

prune1.9s

Filtered

798 candidates to 504 candidates (63.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
0.2b	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
11.2b	(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
428×	`add-sqr-sqrt`
399×	`*-un-lft-identity`
397×	`add-cube-cbrt`
178×	`associate-r`
65×	`add-exp-log`
57×	`div-inv`
38×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
12×	`prod-exp`
11×	`associate-l` `unswap-sqr`
7×	`pow1`
6×	`log-prod` `cbrt-unprod`
4×	`unpow-prod-down` `rec-exp` `1-exp` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `associate-/l/`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `associate-*r/` `pow-prod-down` `pow-exp` `log-pow` `flip--`

Counts

4 → 492

Calls

4 calls:

170.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
113.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
121.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

series669.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
185.0ms	(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
135.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

simplify146.0ms

Algorithm

egg-herbie

Counts

504 → 504

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2117	11875
1	5001	11170

prune1.6s

Filtered

504 candidates to 332 candidates (65.9%)

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b	(* (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n) 100.0)
11.2b	(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite407.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
22×	`associate-l` `add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`associate-r` `prod-exp`
8×	`cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-l/` `associate-/r` `-commutative` `associate-/l`
2×	`div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

135.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
139.0ms	(* (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n) 100.0)
123.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

series704.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
216.0ms	(* (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n) 100.0)
133.0ms	(/ (- (+ (* 1.0 i) (+ (* 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))

simplify74.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	530	1973
1	2389	1671
2	5001	1667

prune382.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 7.0b

regimes413.0ms

Accuracy

51.4% (10.8b remaining)

Error of 21.7b against oracle of 10.9b and baseline of 33.2b

bsearch596.0ms

Steps

Iters	Range		Point
8	4.857585983193909e-119	1.2526148682615025e-114	6.931508871390016e-118
9	-64698196.670160554	-0.37949367736095085	-1.4720208733212128
7	-1117730599.3323822	-64698196.670160554	-1052610260.2415111
8	-1.6575157961979843e+24	-2.0257957255525243e+20	-2.7376334279782315e+20
5	-1.155399601105498e+98	-5.129643794534772e+97	-1.0664791814828006e+98
10	-7.67426779176068e+146	-2.077318348352935e+129	-8.254710623414133e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	97
1	87	97

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.1s	1000×	body	2560	valid
1.8s	2443×	body	1280	valid
465.0ms	1551×	body	640	valid
146.0ms	883×	body	320	valid
137.0ms	3144×	body	80	valid
77.0ms	2296×	body	80	nan
47.0ms	445×	body	160	valid
33.0ms	9×	body	5120	valid