Details

sample204.0ms

Algorithm

intervals

Results

82.0ms	90×	body	1280	valid
61.0ms	27×	body	2560	valid
24.0ms	49×	body	640	valid
10.0ms	100×	body	80	valid
5.0ms	76×	body	80	nan
5.0ms	18×	body	320	valid
3.0ms	17×	body	160	valid

simplify42.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
10.1b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite615.0ms

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:

232.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
129.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
224.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts

4 → 12

Calls

4 calls:

552.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms	(pow (+ 1.0 (/ i n)) n)
357.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1319	3734
1	5002	3446

prune849.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
2.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
72×	`prod-diff`
66×	`add-cube-cbrt`
46×	`unpow-prod-down`
31×	`times-frac`
26×	`distribute-rgt-in` `distribute-lft-in`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r*` `sqr-pow`
11×	`distribute-lft-out`
8×	`fma-neg`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `div-exp` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `div-inv`
2×	`associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

224.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
127.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
148.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

265.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms	(pow (+ 1.0 (/ i n)) n)
356.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify103.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	792	2367
1	3917	1720
2	5002	1708

prune367.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (/ i n) n) 1.0))
0.1b	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
3.1b	(- (pow (/ i n) n) 1.0)
6.3b	(pow (/ i n) n)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

177×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
159×	`add-cube-cbrt`
153×	`prod-diff`
147×	`unpow-prod-down`
132×	`times-frac`
53×	`distribute-rgt-in` `distribute-lft-in`
21×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`fma-neg`
14×	`div-inv`
13×	`associate-/r*` `sqr-pow`
8×	`associate-r` `difference-of-squares`
7×	`pow1` `div-exp`
6×	`cbrt-undiv` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod`
2×	`pow-exp` `associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r/` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 300

Calls

4 calls:

78.0ms	(* 100.0 (- (pow (/ i n) n) 1.0))
61.0ms	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
36.0ms	(- (pow (/ i n) n) 1.0)
3.0ms	(pow (/ i n) n)

series344.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* 100.0 (- (pow (/ i n) n) 1.0))
146.0ms	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
72.0ms	(- (pow (/ i n) n) 1.0)
44.0ms	(pow (/ i n) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1220	3885
1	5002	2868

prune563.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
3.4b	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
6.3b	(pow (/ i n) n)
6.3b	(pow (/ i n) (* 2 n))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
43×	`times-frac`
39×	`unpow-prod-down`
37×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`fma-def`
12×	`add-exp-log`
11×	`distribute-lft-out`
8×	`add-log-exp`
6×	`pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `pow-exp` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
3×	`flip3-+` `div-sub` `div-exp` `flip-+` `sqr-pow`
2×	`neg-sub0` `pow-to-exp` `associate-+r-` `pow-pow` `unsub-neg` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `neg-log` `clear-num`

Counts

4 → 138

Calls

4 calls:

90.0ms	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
27.0ms	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
3.0ms	(pow (/ i n) n)
3.0ms	(pow (/ i n) (* 2 n))

series308.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
78.0ms	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
49.0ms	(pow (/ i n) n)
48.0ms	(pow (/ i n) (* 2 n))

simplify88.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	784	1386
1	3542	1285
2	5001	1280

prune489.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.5b

regimes218.0ms

Accuracy

51.5% (13.2b remaining)

Error of 29.8b against oracle of 16.6b and baseline of 43.9b

bsearch895.0ms

Steps

Iters	Range		Point
8	1.9388806651223434e+173	8.867436241502294e+176	4.7215330661381895e+175
9	3.1383368649600063e-111	2.221497081354824e-102	1.862196599311927e-104
10	-5.360679504985299e-297	2.1728968967176598e-303	-7.7041642639419e-311
7	-3529.757956125628	-29.541817090935037	-29.971639032111977
8	-1.7636691380633754e+18	-2542138303994675.5	-8.549866216582126e+17
8	-5.1499886097089576e+153	-1.8010740352434605e+151	-2.5145781368598933e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	108
1	113	108

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.2s	2457×	body	1280	valid
2.1s	984×	body	2560	valid
701.0ms	1628×	body	640	valid
288.0ms	3001×	body	80	valid
249.0ms	877×	body	320	valid
157.0ms	2279×	body	80	nan
78.0ms	407×	body	160	valid
25.0ms	6×	body	5120	valid