Details

Time bar (total: 34.0s)

sample163.0ms

Algorithm
intervals
Results
63.0ms29×body2560valid
52.0ms81×body1280valid
14.0ms50×body640valid
5.0ms106×body80valid
4.0ms29×body320valid
4.0ms1×body5120valid
3.0ms88×body80nan
1.0ms11×body160valid
1.0ms30×body80overflowed

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite649.0ms

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:
244.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
134.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
239.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
368.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
259.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
226.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune855.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
528×*-un-lft-identity
296×add-sqr-sqrt add-cube-cbrt
116×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
12×unpow-prod-down
8×cbrt-undiv fma-def div-exp add-log-exp
6×pow1 div-sub
4×expm1-log1p-u pow-unpow log1p-expm1-u
3×sqr-pow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 410
Calls
4 calls:
92.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) n)
346.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.7s

Counts
4 → 12
Calls
4 calls:
267.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
220.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
209.0ms
(pow (+ 1.0 (/ i n)) n)
2.0s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify124.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0188610118
150019695

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize27.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
5.8b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite702.0ms

Algorithm
rewrite-expression-head
Rules
3405×times-frac
2121×*-un-lft-identity
1275×add-sqr-sqrt add-cube-cbrt
423×distribute-lft-out
150×div-inv
141×associate-/r/
78×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
9×div-sub
7×pow1
5×pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1190
Calls
4 calls:
13.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
12.0ms
(pow (+ 1.0 (/ i n)) n)
523.0ms
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series15.2s

Counts
4 → 12
Calls
4 calls:
206.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
214.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
207.0ms
(pow (+ 1.0 (/ i n)) n)
14.6s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (- (* 1.0 1.0)) (- (* 1.0 1.0))))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify457.0ms

Algorithm
egg-herbie
Counts
1202 → 1202
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0500157884

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize35.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×unpow-prod-down
10×add-sqr-sqrt add-cube-cbrt
8×pow1 add-exp-log pow-unpow
4×expm1-log1p-u pow-to-exp pow-pow pow-exp add-cbrt-cube log1p-expm1-u distribute-lft-out add-log-exp sqr-pow
Counts
4 → 76
Calls
4 calls:
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
13.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))

series818.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(pow (+ 1.0 (/ i n)) n)
205.0ms
(pow (+ 1.0 (/ i n)) n)
204.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
205.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))

simplify82.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0186496
1760466
23083460
35001444

prune487.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.5b

regimes121.0ms

Accuracy

38.7% (12.8b remaining)

Error of 32.8b against oracle of 19.9b and baseline of 40.9b

bsearch360.0ms

Steps
ItersRangePoint
8
2.164665745185003e+288
3.791162508885093e+291
2.74199199550634e+289
9
1.878323827526276e+218
6.530472444770861e+226
3.451705372151421e+222
10
1.7574313866537943e+136
8.867201874327049e+154
5.484829455183571e+145
8
-2.3691063040732607
-0.001787912586083248
-0.6721696517861357

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0109200
1119200
2127200
3141200
4141200

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s2321×body1280valid
1.4s749×body2560valid
431.0ms1530×body640valid
145.0ms3421×body80valid
128.0ms793×body320valid
77.0ms2473×body80nan
42.0ms1036×body80overflowed
42.0ms414×body160valid
22.0ms6×body5120valid